Pandemic Care for Burn Pits Exposure Act of 2020 This bill requires the Department of Defense and the Department of Veterans Affairs (VA) to ensure that the first health assessment conducted for a member of the Armed Forces or veteran after such an individual tests positive for a virus certified as a pandemic includes an evaluation of whether the individual has been (1) based or stationed at a location where an open burn pit was used, or (2) exposed to toxic airborne chemicals or contaminants relating to service in the Armed Forces. A burn pit is an area used for burning solid waste in open air without equipment. If such an evaluation establishes that an individual was based or stationed at a location where an open burn pit was used, or that the individual was exposed to toxic airborne chemicals or contaminants, the individual must be enrolled in the Airborne Hazards and Open Burn Pit Registry unless they opt out of enrollment. The VA's Airborne Hazards and Burn Pits Center of Excellence must conduct a study on the health impacts of infection with a virus designated as a global pandemic, including the coronavirus (i.e., the virus that causes COVID-19), to members of the Armed Forces and veterans who have been exposed to open burn pits and other toxic exposures. The study must be analyzed to assist in preparation for potential future pandemics.