Service to Country Reimbursement Act of 2003 - Requires the Secretary of the military department concerned (Secretary), at the request of a State or local government that continues to pay all or a portion of the civilian compensation of an employee while that employee is absent due to a call or order to serve on active military duty for a period of more than 30 days, to reimburse the State or local government up to an amount not to exceed the difference between: (1) the amount of civilian compensation that would otherwise have been payable to the employee if the employee's civilian compensation had not been interrupted by active-duty service; and (2) the amount of military pay that is payable to such employee for the active duty service performed. Requires an employee who fails to return to such civilian employment to refund to the Secretary the total amount of reimbursement provided with respect to that employee, but allows the Secretary to waive such refund requirement if such recovery would be against equity and good conscience or contrary to the best interests of the United States. Requires the Secretary to waive such refund if the failure of the employee to report or apply was due to an injury or disability that is not the fault of the employee.