Travel Reimbursement for Inactive Duty Training Personnel (TRIP) Act of 2013 - Directs the Secretary of the military department concerned to reimburse a member of the reserves for transportation expenses incurred in connection with: (1) round-trip travel in excess of 100 miles to an inactive duty training location, regardless of the method of transportation; and (2) round-trip travel of any distance to an inactive duty training location, if such travel requires a commercial method of transportation other than ground transportation. Requires the Secretary, in determining the amount of the allowance or reimbursement, to use the reimbursement rate for the use of privately-owned vehicles by government employees on official business.