The first thing I would do is contact the person who commissioned the quilt. It's her quilt after all. She should be the one to make the decision whether to continue on with the fabric you have or substitute something else. Since the Amazon listing claimed the panels were 100% cotton and it was shipped directly to you, she is probably unaware of the fact that they aren't as advertised and that it might make a difference in the finished quilts appearance and/or feel.
If she wants you to proceed as planned, I'd snip a corner of the questionable fabric and do a burn test just be be absolutely certain that it is indeed polyester before you start figuring out how to work with it.