Grayfield Redevelopment and Economic Advancement Through Effective Repurposing and Revitalization of Shopping Centers Act of 2021 or the GREATER Revitalization of Shopping Centers Act of 2021 This bill allows the Department of Housing and Urban Development (HUD) to make matching grants for projects financed under the Section 108 Loan Guarantee Program in an effort to eliminate blight associated with abandoned shopping centers. The Section 108 Loan Guarantee Program allows HUD to provide loan guarantees to participating Community Development Block Grant recipients. These loan guarantees assist those recipients in financing economic and community development projects. The bill requires the Government Accountability Office to report on the effectiveness of the program and to recommend improvements.