Stopping Improper Payments to Foreigners Act This bill disqualifies resident aliens holding a nonimmigrant visa from eligibility for 2020 recovery rebates provided by the Coronavirus Aid, Relief, and Economic Security Act or the CARES Act. Specifically, it requires the Department of Homeland Security (DHS) to notify the Internal Revenue Service of any individual who receives a nonimmigrant visa during the eligibility period for recovery rebates. DHS must deny visas to any resident aliens who fail to repay a recovery rebate for which they are ineligible.