EB-5 Reform and Integrity Act of 2021 This bill reauthorizes the EB-5 Regional Center program through FY2026 and makes various changes to the program, such as imposing various oversight requirements. (EB-5 visas provide permanent resident status to qualified alien investors. A regional center allows EB-5 aliens to pool investments to meet various investment and job creation requirements.) Oversight-related provisions include requiring each center to (1) notify the Department of Homeland Security (DHS) of proposed changes to the center's structure, (2) maintain certain records and make such records available to DHS for audits, (3) obtain approval for each particular investment offering, and (4) annually report to DHS. The bill prohibits certain individuals and entities from involvement in a center, such as (1) a person who had committed a violation involving fraud in the previous 10 years, (2) a non-U.S. national not admitted for permanent residence, or (3) a foreign government official. DHS shall deny petitions, such as a petition to certify a regional center or to classify an alien as an alien investor, if approval would threaten U.S. national interest. The bill provides various enforcement authority to DHS and U.S. Citizenship and Immigration Services, including the ability to permanently bar an individual from participating in the regional center program. The bill establishes the EB-5 Integrity Fund to fund program enforcement activities. The bill contains various provisions related to EB-5 petitions, such as a provision authorizing DHS to extend an alien's conditional permanent residence status.