Veterans Expedited TSA Screening Safe Travel Act or the VETS Safe Travel Act (Sec. 2) This bill makes certain veterans eligible for the Transportation Security Administration PreCheck Program at no cost if they meet the program's background check and security requirements. Veterans who are eligible for this fee waiver are those who require the use of a wheelchair, prosthetic limb, or other assistive device to aid with mobility due to (1) loss, or loss of use, of a limb; (2) full or partial paralyzation; or (3) permanent blindness.