I bought 3 used button-type quick change transmission bands on Tbay a while back so that I would have an extra set (and to get some practice with before I have to deal with the real thing someday).
They came with old, rotten cotton linings on them, so today I stripped the old linings off. One of the bands had an extra layer of material under the main cotton band, it was about 1/16 inch thick, it looked and felt like cardboard. Did some bands come like this, or was this somebody's home-brew way of getting some extra lining thickness to compensate for a worn drum or something? Sorry, I didn't think to take pictures before I trashed the old linings.
Might have been a worn drum or the drum might have been turned down and the extra thickness might have been added to compensate for adjustment.
I have also seen that recommended when using some standard cotton belting as lining in order to build it up to adequate thickness.
I don't recommend it.
Drive carefully, and enjoy