Restoring the IRS Act This bill provides additional appropriations after FY2021 for the expenses of the Internal Revenue Service (IRS) for taxpayer services, enforcement activities, and business systems modernization. The bill establishes new reporting requirements for certain banks or other financial institutions and increases enforcement penalties for accuracy-related underpayments of tax up to a maximum of 40% of the underpayment for taxpayers with taxable incomes greater than $5 million. The IRS must report to Congress annually on plans to shift more of its auditing and enforcement assets toward high-income tax filers. The report must also include a tax gap analysis and a comprehensive analysis and description of whether there are any racial disparities in its enforcement activities or audits. The bill also applies false claims rules to claims, records, or statements made by taxpayers whose gross income equals or exceeds $10 million for the taxable year, and the damages sustained by the government due to such false claims exceed $1 million.