Why would a customer want to be able to take apart a jigsaw puzzle? Maybe she's only concerned about evidence of adhesive or some other visible change to the appearance of it. Some conversation at the design table might change her mind, especially when she realizes that her specification would substantially increase the price of the framing.
My preference would be to vacuum-wet mount it to 4-ply board, reinforced by fluted polypropylene. My second choice would be to vacuum-dry mount it to a reversible, pre-adhesive board using low-temperature, short dwell-time adhesive, such as Kool Tack.
Anyway, this customer wants to be able to take it apart. That certainly can be done, and it would be an easy, very profitable framing job. As Randy said, DCO mounting would be the best choice. Since the puzzle is so large, it would be very important to use rigid materials. In my DCO design for this project, the backing would be 3 mm or 4 mm aluminum composite material (DiBond, ePanel, Alucobond, etc.) and the glazing would be at least 6 mm acrylic. If matting is involved, be sure to construct a sturdy sink-mount on the backing board to tightly retain the puzzle's edges, and butt the mat opening up to the edges of the puzzle, which must be pressed against the acrylic.