Supporting Expanded Review for Veterans In Combat Environments Act of 2021 or the SERVICE Act of 2021 This bill expands eligibility for Veterans Health Administration mammography screenings to veterans who served in certain locations during specified periods, including those who were exposed to toxic substances at such locations. The specified locations and corresponding time periods include Iraq between August 2, 1990, and February 28, 1991, and from March 19, 2003, until burn pits (areas used for burning solid waste in open air without equipment) are no longer used in Iraq; the Southwest Asia theater of operations, including Kuwait, Saudi Arabia, Oman, and Qatar, from August 2, 1990, until burn pits are no longer used in such locations; and Afghanistan, Djibouti, Syria, Jordan, Egypt, Lebanon, and Yemen from September 11, 2001, until burn pits are no longer used in such locations; and other locations and time periods as determined by the Airborne Hazards and Open Burn Pit Registry. The bill specifies that the listed locations do not include bodies of water around or airspace above such locations.