Removing Extraneous Loopholes Insuring Every Veteran Emergency Act or the RELIEVE Act This bill expands eligibility for Department of Veterans Affairs (VA) reimbursement of emergency treatment for veterans who are treated in a non-VA facility. Specifically, the bill waives the requirement that a veteran must have received VA care within the 24-month period preceding the furnishing of emergency treatment if the veteran receives such emergency treatment within the 60-day period following their enrollment in the VA health care system.