I have not read all the responses, so I apologize if I am repeating anyone. If you decide that nothing else works and you want to wash the fabric, Start with gentle handwashing, of course. For drying, I've heard that a salad spinner can be used to partially dry small pieces of fabric, then drip dry the rest of the way. This should help limit the fraying involved in washing/drying in the machine.
My LQS owner was telling me she has heard from so many people that buying quilts on line isn't worth it. The quilts are many times smoke-laden or damaged.
Good luck with your little project!