ORDER
Russell and Nancy Zeidler have appealed from a district court order requiring them to reimburse A & W Restaurants, Inc. (“A & W”) for the fees that A & W incurred in successfully defending a prior appeal in this case and in collecting a previous fee award. Pursuant to Seventh Circuit Operating Procedure 6(b), this appeal has been assigned to the panel of judges that heard the prior appeal. Neither the Zeidlers nor A & W have indicated that oral argument is necessary (see Fed. R.App. P. 34(a)(1); Circuit Rule 34(f)), and we have determined that oral argument would not significantly aid the decisional process (Fed. R.App. P. 34(a)(2)(C)). Having reviewed the record and the parties’ briefs, we affirm the district court’s decision.
I.
The Zeidlers operated an A & W franchise from 1993 to 1998. In April 1999, the Zeidlers sued A & W and certain of its officers for wrongful termination of their franchise agreement. In January 2001, the district court granted A & W’s motion for summary judgment and denied the Zeidlers’ cross-motion for partial summary judgment. R. 60, 61; 2001 WL 62571 (N.D.Ill. Jan.25, 2001). The Zeidlers appealed the district court decision, and in August 2002, this court affirmed that decision. 301 F.3d 572 (7th Cir.2002).
The franchise agreement between the Zeidlers and A & W contained a provision obligating the Zeidlers, in the event that A & W prevailed in litigation arising under the agreement, to pay A & W’s attorney’s fees and related non-taxable expenses. R. 37 Ex. A at 22, § 17.3. Pursuant to that provision, the district court in May 2001 granted in part A & W’s motion for the fees and costs it had incurred through *597summary judgment. The court awarded A & W fees in the amount of $150,000, taxable costs (see 28 U.S.C. § 1920) in the amount of $2,475.13, and non-taxable costs (travel-related expenses) in the amount of $758.09, for a total award of $153,233.22. R. 78; 2001 WL 561367 (N.D.I11. May 21, 2001).1 More than a year later, on June 20, 2002, the court reduced that award to a separate judgment on A & W’s motion pursuant to Fed.R.Civ.P. 58(a) (R. 90, 91), and the judgment was docketed on July 9, 2002 (R. 93) (we shall refer to this judgment as the “June 20th judgment”). At some point in late August or early September 2002, the Zeidlers finally satisfied the June 20th judgment after a number of unsuccessful efforts to avoid it. See R. 106 U 2,108 at 3 n. 1. By this time, the Zeidlers had lost their appeal of the summary judgment ruling in this court.
In November 2002, on the heels of its appellate victory, A & W filed a supplemental request for the attorney’s fees it had incurred in connection with both the appeal as well as its efforts to enforce the June 20th judgment. R. 112. A & W sought a total supplemental fee award of $76,625.10, ninety percent of which reflected the fees it had incurred in connection with the appeal.
The Zeidlers opposed A & W’s fee request. R. 113. In part, they contended that A & W’s attorneys had behaved improperly in their dealings with Andrew Hester. Id. at 1-5. To place this argument in context, some additional background is necessary.
Early in the litigation, the Zeidlers had engaged Hester, who has a background in the restaurant industry, as their expert. Hester and the Zeidlers parted ways, however, after he prepared a report opining that the Zeidlers had failed to properly manage and maintain their restaurant. Hester then contacted A & W’s attorneys and disclosed his findings to them. A & W’s lawyers subsequently drafted an affidavit detailing his course of dealing with the Zeidlers and their counsel along with his findings. Hester signed that affidavit, and A & W submitted the affidavit along with a copy of his report in support of its motion for summary judgment. R. 37 vol. 1, Declaration D. The Zeidlers moved to strike Hester’s affidavit and for sanctions, charging Hester, A & W, and the company’s counsel with bad faith and other improprieties. R. 44.
In ruling on A & W’s motion for summary judgment, the district court found it unnecessary to take Hester’s affidavit into consideration. “Because the Court did not consider or rely upon Hester’s affidavit in reaching its conclusions, plaintiffs’ motion to strike is denied as moot.” 2001 WL 62571, at *1.
The Zeidlers did not let the matter of Hester’s affidavit drop, however. Mr. Zeidler raised it again in opposition to A & W’s first request for an award of attorney’s fees and costs. See R. 73, 76. In its opinion on that request, the district court agreed that it was improper for Hester to contact A & W’s counsel, and the court also allowed that A & W’s attorneys may have been imprudent in communicating with Hester without first seeking guidance from the court. 2001 WL 561367, at *6. However, because the court had disregarded Hester’s affidavit when it granted A & W’s summary judgment motion, the court saw no need to delve into the matter further. Id. at *5-*6.
In August 2001, the Zeidlers’ attorney took Hester’s deposition in state-court litigation that Hester had initiated against *598Russell Zeidler. In that deposition, Hester acknowledged that certain of the statements in the affidavit that A & W’s counsel had drafted and that he had signed did not accurately reflect facts that were within his own knowledge and/or that he had conveyed to A & W’s attorneys. See generally R. 92 Ex. H at 121-169; see, e.g., id. at 130, 140, 220.
Now armed with Hester’s deposition, Russell Zeidler renewed the accusations of impropriety when, in June 2002, A & W asked the district court to formally enter judgment on the $153,233.22 in fees and costs that the court had awarded to A & W the previous May. In his belated response to that request, Mr. Zeidler contended that the deposition evidenced not only perjury on Hester’s part, but the knowledge and complicity of A & W’s lawyers in that perjury. R. 92. Mr. Zeidler -urged the court to vacate its May 2001 award of fees and costs to A & W and order an investigation into the matter. Id. The court construed Mr. Zeidler’s opposition, which was not filed until after the court had already granted A & W’s motion to enter judgment, as a motion to vacate the June 20th judgment. R. 119-3 at 3. In oral remarks on the matter, the court indicated that it had read Hester’s deposition in its entirety but had found nothing in the deposition that would warrant vacating the judgment for attorney’s fees in A & W’s favor. Id.
On September 4, 2002, Russell Zeidler filed a pro se petition for rehearing in this court asking us to reconsider our ruling on the summary judgment appeal. He attached to the petition a copy of the transcript of Hester’s deposition. He argued, among other things, that A & W’s attorneys had suborned perjury in preparing Hester’s affidavit and that the grant of summary judgment in A & W’s favor was therefore improper. No. 01-1341, Petition for Rehearing at 2-5.2 This court denied Mr. Zeidler’s rehearing petition on September 12, 2002. 45 Fed.Appx. 546 (7th Cir.2002).
In sum, the circumstances surrounding Hester’s affidavit had already been raised on multiple occasions when, in November 2002, A & W filed its second request for fees. Again citing Hester’s deposition, the Zeidlers posited that A & W’s attorneys had conspired with Hester, and possibly with other witnesses as well, to manufacture evidence in order to secure a victory for A & W.R. 113 at 1-5. Arguing that A & W’s hands consequently were unclean, the Zeidlers urged the court to deny the company’s second fee request.
Again, the district court was unmoved by the Zeidlers’ argument. In its February 2003 order partially granting A & W’s supplemental fee request, the court noted that it had previously considered and rejected the Zeidlers’ contention that fees should be denied to A & W based on the purported misconduct of its counsel; it added that the Zeidlers had presented no new evidence in support of this contention. R. 115. “In short, [the Zeidlers’] claims of misconduct provide no basis for refusing or cutting A & W’s fees for the appeal or the attempt to collect the judgment.” Id. *599The district court did find persuasive the Zeidlers’ alternative contention that the fees claimed by A & W were excessive. Noting that A & W’s counsel claimed to have spent some 236 hours defending the Zeidlers’ appeal — which time accounted for approximately $69,000 of the $76,000 that A & W sought — the court found the hours expended unreasonably high by one-third. Id. It therefore reduced the fees claimed for the appeal by $19,200. After finding the $8,500 in fees claimed for collecting the June 20th judgment to be reasonable, the court awarded A & W total fees in the amount of $57, 425.10. Id.
From the supplemental fee award, the Zeidlers appeal.
II.
Where the basis for an award of attorney’s fees is contractual, the amount of fees to which a party is entitled constitutes a question of contract interpretation. Bowles v. Quantum Chem. Co., 266 F.3d 622, 636 (7th Cir.2001). In this case, the franchise agreement provides that A & W is entitled to its fees and costs but is silent as to whether that entitlement extends to any and all costs incurred by A & W or is limited to reasonable fees and costs. Compare id. at 636 (severance plan required company to pay “all legal fees and expenses incurred”) with Chojnacki v. Georgia-Pacific Corp., 108 F.3d 810, 814 & 818 (7th Cir.1997) (contract entitled plaintiff to “all reasonable legal fees and expenses actually incurred”). However, we have recognized with approval that “courts interpolate the word ‘reasonable’ into clauses of this kind.” Balcor Real Estate Holdings, Inc. v. Walentas-Phoenix Corp., 73 F.3d 150, 153 (7th Cir.1996); see also Med-com Holding Co. v. Baxter Travenol Labs., Inc., 200 F.3d 518, 521 (7th Cir.1999). That is precisely what the district court did here in quantifying the fees for which the Zeidlers were obligated to indemnify A & W.R. 115; see also 2001 WL 561367, at *3-*4. The district court’s judgment as to the quantum of fees that is reasonable is a discretionary one to which we defer. Balcor, 73 F.3d at 153; see also Harter v. Iowa Grain Co., 220 F.3d 544, 562 (7th Cir.2000).
The Zeidlers do not dispute the method by which the trial judge calculated the supplemental fee award. Instead, they contend that the trial court abused its discretion by awarding fees to a party with “unclean hands.” The Zeidlers do not cite any authority in support of this claim; indeed, their briefs are devoid of any precedential citations whatsoever. See Fed. R.App. P. 28(a)(9)(A) (requiring arguments in appellant’s brief to include “citations to the authorities and parts of the record on which the appellant relies”); see also, e.g., Tyler v. Runyon, 70 F.3d 458, 464-65 (7th Cir.1995) (finding argument forfeited where not supported by citation to pertinent authority).
However, it is a well-established maxim that “he who comes in equity must come with clean hands.” Precision Instrument Mfg. Co. v. Automotive Maintenance Mach. Co., 324 U.S. 806, 814, 65 S.Ct. 993, 997, 89 L.Ed. 1381 (1945). The “clean hands” doctrine operates to deny recovery to one who is “tainted with inequitableness or bad faith relative to the matter in which he seeks relief, however improper may have been the behavior of the defendant.” Ibid. Trial courts thus may, in the exercise of their discretion, refuse relief to litigants whose hands they find to be unclean. Id. at 815, 65 S.Ct. at 997-998. Therefore, the issue before this Court is whether or not the district court abused its discretion by granting A & W’s motion for supplemental attorney’s fees notwithstanding the Zeidlers allegations of impropriety in connection with the Hester affidavit.
*600Hester acknowledged in his deposition that the affidavit drafted by A & W’s counsel included some averments that were not within the scope of his own knowledge. See, e.g., R. 92 Ex. H at 130, 140, 220. However, Hester also admitted that he both read and signed the affidavit prepared by A & W counsel, thereby certifying that its contents were true. E.g., id. at 121-22, 153-55. Hester’s deposition also is ambiguous as to what, exactly, he communicated to A & W’s attorneys and vice-versa, and the record thus remains unilluminating as to where the fault lies for the inaccuracies in his affidavit. Consequently, we cannot determine whether or not there is evidence of wrongdoing or “unclean hands” on the part of A & W and/or its counsel.
Yet, a better understanding of the facts underlying Hester’s affidavit is not necessary to determine whether or not the district court abused its discretion, in view of the fact that the district court refused to consider Hester’s affidavit in the first place. Immediately after A & W submitted Hester’s affidavit in support of its motion for summary judgment, the Zeidlers protested the legitimacy of the affidavit and asked the district court to strike it. In ruling on the summary judgment motion, the district judge found it unnecessary to consider Hester’s affidavit and therefore disregarded it altogether. In so doing, the district court took one of the very steps it might have taken — indeed, the most obvious step — had it found that A & W acted improperly in consulting with Hester and preparing his affidavit for submission to the court. See Taylor v. Illinois, 484 U.S. 400, 414, 108 S.Ct. 646, 655, 98 L.Ed.2d 798 (1988). Indeed, the Zeidlers were placed in the very same position that they would have been had the court granted their motion to strike: the affidavit was not considered, and they suffered no discernable harm on account of the affidavit. Any falsehoods in the affidavit, and any improprieties committed in preparing that affidavit, were in this way dealt with early on in the litigation. Denying A & W’s supplemental request for attorney’s fees based on its purportedly unclean hands would have the practical effect of serving as a secondary sanction against A & W.
We are not saying that the district court could not have sanctioned A & W in this way had it looked into the matter further and found that A & W and/or its attorneys were guilty of impropriety in connection with Hester’s affidavit. Courts have the inherent authority to sanction abuse of the judicial process, Chambers v. NASCO, Inc., 501 U.S. 32, 43, 111 S.Ct. 2123, 2132, 115 L.Ed.2d 27 (1991), and enjoy discretion in selecting the most appropriate form of sanction, id. at 44-45, 111 S.Ct. at 2132-33; see Thomas v. General Motors Acceptance Corp., 288 F.3d 305, 308 (7th Cir.2002). Denying A & W the fees to which it otherwise would have been entitled under the franchise agreement (or reducing the amount of the fee award) would have been an appropriate measure for the court to consider as a sanction for any wrongdoing vis á vis Hester’s affidavit. However, given that the court had removed Hester’s affidavit from consideration early in the litigation and allowed it to have absolutely no bearing on the outcome of the suit, we cannot say that it was an abuse of discretion for the court to decide that it was unnecessary to look more closely into the Hester situation or to decide that denying A & W its fees was unwarranted on the record as it stands.
The district court’s decision particularly was not an abuse of discretion given its chronological context. A & W had filed Hester’s affidavit in September 2000 in support of its successful motion for summary judgment. The district court award*601ed A & W its fees up to and including that motion in May of 2001. As we have noted, the Zeidlers ultimately withdrew their appeal of that award. Supra n. 1. The Zeidlers did not separately appeal the June 20th judgment that the court entered on the fee award the following year, although by that time the Zeidlers had Hester’s deposition in hand and, in fact, had cited Hester’s deposition testimony in opposition to the June 20th judgment. The fees that A & W sought in November 2002 were primarily for the Zeidlers’ unsuccessful summary judgment appeal — in which the Hester situation was not raised (see supra n. 2) — and for A & W’s efforts to collect the June 20th judgment. There is no indication that any impropriety occurred in those additional proceedings. Whatever misconduct allegedly occurred in connection with the Hester affidavit had a remote connection, at best, with A & W’s second fee request.
Moreover, the district court had, by this time, already considered and rejected the Zeidlers’ allegations as to Hester on multiple occasions. The Zeidlers had no meaningful additional evidence to present in support of their allegations when they opposed A & W’s supplemental fee request. They had already presented Hester’s deposition to the court when they opposed the June 20th judgment on the first fee award; Mr. Zeidler had, for that matter, already presented the deposition to this court in support of his petition for rehearing. Neither the deposition nor anything else that the Zeidlers cited in opposing the supplemental fee request was new or different from what had been raised before. Consequently, the district court acted well within its discretion to conclude that the circumstances surrounding Hester’s affidavit did not constitute a basis for denying A & W’s supplemental fee request.
III.
For the foregoing reasons, we conclude that the district court did not abuse its discretion by awarding supplemental fees to A & W. We therefore AFFIRM the district court’s judgment.
. The Zeidlers took an appeal from the May 21 decision (No. 01-2551), but we later dismissed that appeal on the Zeidlers’ motion pursuant to Fed. R.App. P. 42(b).
. Notably, however, the Zeidlers had barely mentioned the Hester situation in their appellate briefs. They had simply suggested in a footnote that in failing to consider Hester’s affidavit, the district court had overlooked evidence that was favorable to the Zeidlers. No. 01-1341, Appellants’ Opening Br. at 9-10 n. 2. It was rather ironic for the Zeidlers to make that suggestion, as A & W was quick to point out, given that the Zeidlers themselves had moved to strike Hester’s affidavit. Appellee's Br. at 4 n. 2. In any case, the Zeidlers had not raised the district court’s handling of the affidavit, or any of the alleged improprieties concerning that affidavit, as an issue in the appeal. Appellants’ Opening Br. at 3 (Statement of Issues).