Refund to Rainy Day Savings Act This bill requires the Department of the Treasury to establish and implement a Refund to Rainy Day Savings Program to permit a taxpayer to defer payment on 20% of a tax refund to be deposited into a Treasury account, accumulate interest, and disbursed to the taxpayer in six months. The bill also reauthorizes the Assets for Independence (AFI) federal matched savings program through FY2024 and requires appropriations for the program to be reserved for general research and evaluation, grants for AFI innovation projects to expand the availability of matched savings accounts to low-income individuals, and a three-year matched savings account pilot program established by the Department of Health and Human Services (HHS) to encourage savings by low-income taxpayers. Under the pilot program, HHS may provide grants to qualified entities to match funds saved by low-income taxpayers under the Refund to Rainy Day Savings Program. Qualified entities for the pilot program include nonprofit organizations, state or local government agencies or tribal governments applying with a nonprofit organization, sites that offer free tax assistance under certain Internal Revenue Service programs, and certain low-income credit unions and community development financial institutions. HHS must (1) contract with an independent research organization to evaluate the pilot program, and (2) report annually to Congress on the progress and outcomes of the pilot program.