Effectively up to ten (10) years back. For all practical purposes, how far back you can claim is defined by the statute of limitations, or time within which you'd have to file a lawsuit if they don't voluntarily pay you (since only a lawsuit can force them to pay). A claim for reimbursement is considered a "contract" claim--it arises out of the agreement, whether written or oral, under which you would travel for work and foot the costs up front in exchange for reimbursement. That statute of limitations is 10 years in your state (LA).