It's the carry strap from one of the 2-quart plastic bladder canteens, found in both olive drab and desert tan.
FYI, my sweetie was a USAF avionics tech for the Pave Penny laser targeting pod in the A10, now made hopelessly obsolete by the LANTIRN laser designator and targeting pods. She too is fond of *things that go bang* that come from the sky, are too big for slings, and which you don't want to drop on your big toe.