I agree with all those who suggested misting with water. If the holes aren't too big, I find that misting with room temperature water & gently rubbing with a soft white cloth usually does the trick. Just be sure to let it dry completely before you start quilting again as cotton fibers stretch when wet & you can accidentally pull it out of shape.

When I need to pick out stitching, I use my stitch picker to undo two or three stitches, then use my (forceps - tweezers)to hold those stitches on the top side, if you gently pull very lightly, the other side bobbin thread it will come to the top, I continue to gently lifted on the threads in the (forceps-tweezers) and once I get bobbin thread about three inches long, snip it off, again lift the thread in the (forceps-tweezers)gently and carry on taking out the bobbin stitches. Once I have the stitches out, I use a plastic flat edge to flatten the holes, if there are any.....

I had an aunt that was a matron (nurse) and she gave me my forceps............You could probably purchase forceps at a medical store.........plastic flat edge (plastic knife).