SUMMARY ORDER
Mario Guzman, a native and citizen of Mexico, seeks review of a March 23, 2011 order of the BIA affirming the May 24, 2010 decision of Immigration Judge (“IJ”) Alan A. Vomacka, finding Guzman removable and ineligible for cancellation of removal. In re Mario Guzman, No. A088 207 986 (B.I.A. Mar. 23, 2011), aff'g No. A088 207 986 (Immig.Ct.N.Y.C., May 24, 2010). We assume the parties’ familiarity with the underlying facts and procedural history in this case, which we reference only as necessary to explain our decision to deny the petition for review.
Under the circumstances of this case, we have reviewed the IJ’s decision as supplemented and modified by the BIA. See Xue Hong Yang v. U.S. Dep’t of Justice, 426 F.3d 520, 522 (2d Cir.2005); Yan Chen v. Gonzales, 417 F.3d 268, 271 (2d Cir.2005). For Guzman, who is not a lawful permanent resident, to demonstrate eligibility for cancellation of removal, he must show that his “removal would result in exceptional and extremely unusual hardship to [his] spouse, parent, or child, who is a citizen of the United States or an alien lawfully admitted for permanent residence.” 8 U.S.C. § 1229b(b)(1). Guzman challenges the agency’s conclusion that he failed to carry this burden with respect to his U.S. citizen son. He asserts that the BIA erred as a matter of law in mischaracterizing the record to support an erroneous conclusion that, if Guzman were removed, his wife and two U.S. citizen children would remain the United States rather than accompany him to Mexico. We retain jurisdiction to consider this alleged legal error. See 8 U.S.C. § 1252(a)(2)(B), (D); Mendez v. Holder, 566 F.3d 316, 322-23 (2d Cir.2009).
*92 1. Hardship Determination
We agree with Guzman that the BIA mischaracterized the IJ’s decision when it referred to the IJ’s “finding that ... the respondent’s wife ... would remain for the time being in the United States with the couple’s children.” J.A. 3. While the IJ expressed the opinion that this was likely, see J.A. 50, he made no definite finding as to the intent of Guzman’s wife. Insofar as the BIA’s mischaracterization might be construed as making a de novo finding of fact rather than reviewing the IJ’s findings for clear error, that would run afoul of the limited scope of review assigned to the BIA by 8 C.F.R. § 1003.1(d)(3)(i). See Hui Lin Huang v. Holder, 677 F.3d 130 (2d Cir.2012). However, this error would not require remand, because there is no realistic possibility that the BIA would reach a different conclusion absent the mischaracterization.
We know that this is so because Guzman’s appeal to the BIA relied on the very factual premise that he now faults the agency for adopting — i.e., his son’s remaining in the United States after Guzman’s removal to Mexico. In his brief to the BIA, Guzman argued that this “loss of a father” would pose a particular hardship to his son because the boy suffers from Attention Deficit Disorder. J.A. 26-28. On this record, there is “no realistic possibility” that, absent the identified error, the BIA “would have reached a different conclusion,” Alam v. Gonzales, 438 F.3d 184, 187-88 (2d Cir.2006) (internal citations and quotation marks omitted). In such a case, remand is futile. See Cao He Lin v. U.S. Dep’t of Justice, 428 F.3d 391, 401-02 (2d Cir.2005).
2. Exhaustion
Alternatively, Guzman challenges the denial of cancellation on the ground that his son would suffer hardship if the entire family were to relocate to Mexico. Because Guzman failed to raise this argument before the agency, and because the government here raises this failure to exhaust, we decline to consider the issue. See Lin Zhong v. U.S. Dep’t of Justice, 480 F.3d 104, 124 (2d Cir.2007) (describing issue-exhaustion requirement as “affirmative defense subject to waiver”).
For the foregoing reasons, the petition for review is DENIED. As we have completed our review, any pending motion for a stay of removal in this petition is DENIED as moot. Any. pending request for oral argument in this petition is DENIED • in accordance with Federal Rule of Appellate Procedure 34(a)(2) and Second Circuit Local Rule 34.1(b).