I actually tried GooGone before reading the above post. It didn't touch it. But did make a lovely stain on the back of the quilt to deal with as well.
I took the batting back to Hobby Lobby this morning. I had bought it with a 40% off coupon. But the salewoman gave me a full price store credit for my troubles. They are such a great organization.
It doesn't fix the quilt, but it was nice of her anyway.
The representative of June Tailor is now asking me to send her the quilt after I told her the cleaners said they couldn't get it out. So if she will pay the shipping I'll send it. She said they can always get it out. I say "go for it then"