Background Check Point of Contact Act of 2020 This bill authorizes the Department of Justice to make annual grants to an eligible state that establishes or maintains a point-of-contact system for a licensed firearms importer, manufacturer, or dealer to verify that a firearm sale or transfer would be lawful. To be eligible for such a grant, the state shall meet certain requirements related to the system, including (1) prohibiting a sale or transfer from being completed unless the parties to the transaction receive an approval from the system within 10 days of the start of the transaction; (2) operating a hotline for contacting the National Instant Criminal Background Check System (NICS), for use by licensed firearms importers, manufacturers, and dealers; and (3) publishing an annual report with certain information from the system and information substantially similar to the information found in a NICS operations report.