Pandemic TANF Assistance Act This bill temporarily suspends certain Temporary Assistance for Needy Families (TANF) program requirements and establishes a grant program in response to the COVID-19 (i.e., coronavirus disease 2019) emergency. Specifically, states, tribes, and territories may not deny, reduce, or terminate TANF assistance because a recipient does not meet specified conditions of TANF participation from October 1, 2019, to November 30, 2020. These conditions include time limits for receiving assistance, work requirements, and compliance with paternity establishment or child support procedures. During that time period, the bill also restricts the Department of Health and Human Services (HHS) from penalizing jurisdictions that fail to meet TANF requirements such as work participation standards. However, HHS may reduce grants for jurisdictions that improperly deny, reduce, or terminate TANF assistance in violation of the bill. Additionally, HHS must award grants to states, tribes, and territories for short-term cash, noncash, and in-kind assistance and other activities to assist families meet their basic needs from April 1, 2020, to September 30, 2021. Families eligible for assistance must be impacted by COVID-19 and have monthly income at or below 200% of the federal poverty level. The bill provides funding for this purpose.