Health Care for Burn Pit Veterans Act This bill updates policies and procedures related to Department of Veterans Affairs (VA) health care and benefits for veterans who have been exposed to toxic substances. Specifically, the bill extends the eligibility period for VA hospital care, medical services, and nursing home care for combat veterans who served after September 11, 2001, and were exposed to toxic substances, radiation, or other conditions, including those who did not enroll to receive VA care during the eligibility period. The VA must incorporate into its existing health care screening a screening to help determine potential exposures to toxic substances during military service. Among other requirements, the VA must also provide annual training to health care and benefits personnel with respect to veterans who were exposed to toxic substances; analyze total and respiratory disease mortality in veterans who served in specified locations on specified dates; conduct an epidemiological study on the health trends of veterans who served in the Armed Forces after September 11, 2001; conduct a study to determine trends in the rates of the incidence of cancer in veterans; publish a list of VA resources for veterans who were exposed to toxic substances, families and caregivers of such veterans, and survivors of such veterans who are receiving death benefits; and report on the data quality of the Individual Longitudinal Exposure Record and its usefulness in supporting veterans in receiving VA health care and benefits.