Transparency and Accountability in Health Care Costs and Prices Act of 2020 This bill requires the Department of Health and Human Services (HHS) to provide grants for states to establish and maintain all-payer claims databases. All-payer claims databases collect and publish health care claims data from various payers for such services, including private insurance plans, government employee plans, Medicare, and Medicaid. HHS must prioritize awarding grants to states that, among other things, require mandatory reporting of claims data. Further, the bill permits states to require self-insured employer plans to submit claims data to the state's all-payer claims database.