Veterans Pensions Protection Act of 2013 - Excludes from annual income, for purposes of eligibility for pensions for veterans and their surviving spouses and children, reimbursements resulting from: (1) any accident; (2) any theft or loss; (3) any casualty loss; (4) medical expenses resulting from any such accident, theft, or loss; and (5) pain and suffering (including insurance settlement payments and general damages awarded by a court) related to such accident, theft, or loss.