Not sure where you read about tissue paper and spraying it with 505. I know you posted a while back about golden threads paper which is very different from tissue paper like you use to wrap clothing in gifts. Anyway, what has happened here looks like my fears and concerns I warned you about in that topic came to be.
In addition it looks like you may have another issue going on. If I were to take a wild guess, I am thinking this may be remnants of adhesive from the 505 and possibly even some bearding from the backing. Thinking the 505 may have soaked through your top fabric when gluing the tissue paper and when the process of tearing the paper away may have brought some of those batting fibers up to the top of the quilt. It's also possible that if you used regular tissue paper, which tends to have fine little paper fibers in it, this is just more remnants of it.
If it is rubbing away when you work at it, then I would go buy some shelf lining paper, the kind that has adhesive on it (Walmart has it in the housewares or hardware area) and you peel a backing away to stick to the shelf. Cut a small piece to test! Peel and stick the shelf paper to one of the fuzzy spots, rub it a bit with your hands and then peel it up right away. If it works do it with bigger pieces. It goes much faster than using masking tape and has much more stick to it than sticky tape rollers. You can usually do several peel and sticks, peel up and stick somewhere else before it is covered with little fibers and lint and won't pick up anything anymore. But please test a small area first because if this is batting bearding my solution will only make it worse.
Edited to add is this a t-shirt quilt? If so the nature of the fine rib knit of t-shirt material may also be coming into play here.
Last edited by feline fanatic; 12-15-2018 at 08:38 PM.