EIDL Oversight Act of 2021 This bill establishes oversight requirements for economic injury disaster loans and advances made on those loans. Such requirements include directing the Small Business Administration (SBA) to (1) ensure that loan and advance proceeds are deposited in a legitimate account of a borrower, (2) ensure that any modification of a request for a loan or an advance is reviewed by an SBA employee, and (3) verify the legitimacy of loan or advance applicants through tax returns or other documentation.