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This looks like the scrim layer of the batting that was in that quilt "sandwich". Scrim is added to the batting to help prevent migration of the batting during laundering (there is also batting without scrim), and it is almost always a polyester, for durability (yes, even some marked 100% cotton!). You would need to pick at it, or use a clothing shaver https://a.co/d/0fZavLFv but beware, the batting has lost it's integrity, and it could bunch up on you as you launder the jacket. The tighter the quilting stitch pattern, the better. So, the previous owner/user of this quilt must have washed the heck out of it! It also seem that it was under particular repeated stress in one area, since it doesn't appear to be evenly worn. Maybe kids used it to exit the top bunk like they were making a jail-break... maybe they used it for a pet on a rough concrete surface... or maybe they used it to wrap up their tuba while traveling from gig to gig!? Hard to say. 😏🙋🏼‍♀️❤️