Assistance for Firms Harmed by Tariffs on Exports Act This bill provides financial assistance to companies harmed by retaliatory foreign tariffs. Specifically, it expands the Trade Adjustment Assistance for Firms program, which currently provides such assistance to companies adversely affected by competing imported goods and services. The bill authorizes companies that have seen a significant decrease in sales of exported goods or services, in whole or in part as a result of tariffs imposed by foreign countries in response to U.S. tariff increases, to petition the Department of Commerce for trade adjustment assistance.