If it's this batting:
http://www.joann.com/fusible-polyest...prd_06194716a/
then the fusible is water soluble. I think you could test by wiping your needle down with water to see if it takes the gunk off. If it does, then *maybe* soaking the quilt in the bathtub (since you have already done SITD around all the squares) would dissolve the fusible on the batting. If trying this, I would use a lot of water in the tub, and I would dry the quilt by laying it flat (on a large flat sheet) and putting a fan on it.