Why would it being a take-down require any sort of special backing? Modern bows use fiberglass because that's what they are all made with, take-down or not.
Take-downs that are made of wood have limbs that are also made of wood in 5 pieces that are kind of sandwiched: 2 thin laminates, a wedge in the middle, and the backing on both the back and the belly. The most modern, and most durable, backing is the bow-tuff fiberglass which is not that much thicker than duct tape or fabric.
What I like about this style of bow is that there's more artistic freedom. The riser just just a rigid block, so one can just epoxy a bunch of hardwood pieces together in an arrangement that will look beautiful once all the cutting, rasping, sanding and finishing is done. Then the limbs offer more options regarding the draw weight & length. It's just a matter of how their cut. The backing was my only concern