Toxic Exposure in the American Military Act or the TEAM Act This bill requires the Department of Veterans Affairs (VA) to expand health care, benefits, and resources for veterans with conditions related to exposure to toxic substances. Specifically, the bill expands eligibility for VA hospital care, medical services, and nursing home care to include veterans who (1) were exposed to toxic substances, radiation, or other conditions, and were awarded certain medals (e.g., the Armed Forces Service Medal); (2) are eligible for inclusion in the Airborne Hazards and Open Burn Pit Registry; or (3) have been identified by the Department of Defense to have been possibly exposed during service to an open burn pit, toxic substance, or specified hazardous sites. (A burn pit is an area used for burning solid waste in open air without equipment.) The bill establishes a presumption of service-connection for diseases associated with exposure to certain toxic substances and that become manifest within a certain time period; the VA must specify such diseases and requirements through regulations. Under a presumption of service-connection, specific conditions diagnosed in certain veterans are presumed to have been caused by the circumstances of their military service. Health care benefits and disability compensation may then be awarded. The bill also requires the VA to take specified actions to (1) evaluate scientific evidence regarding associations between diseases and exposure to toxic substances; (2) train its health care personnel on identifying, treating, and assessing illnesses related to such exposure; and (3) provide resources to veterans exposed to toxic substances.