Supporting Care for Dual Eligibles Act This bill establishes and provides funds for grants to support the provision of services to those who are dually eligible for Medicare and Medicaid. Specifically, the bill establishes and provides funds for FY2022 for the Dual Eligible Quality Care Fund. The Centers for Medicare & Medicaid Services (CMS) must use the funds for grants to state Medicaid programs to support quality integrated care for dual eligible beneficiaries, including technology improvements, staff support, and administrative services for beneficiaries. The bill also requires the CMS to biennially audit state Medicaid programs with respect to improper payments; states must also submit plans for mitigating improper payments.