Ok, so I tore off a small piece of the wrap on the underside of the bass drum.
Unfortunately, there's no original wrap underneath, just stringy Luan (vertical grain) all full of glue. Thanks for the advice regarding the lugs' brittleness - they seemed pretty heavy and solid to me, but after removing one I think I know what you're talking about.
The question is: do I bother with removing the wrap and then trying to make the wood look good by hours of sandpapering and lacquering, only to sell the kit for a few bucks, as it's, after all, fairly cheap? I kinda hate this wrap, but at the very least, it's in fairly good shape and lacquering the bare wood seems like an uncertain endeavour to me.