I have taken a quilt apart - it was one my friend made for her Dad. She used a sheet on the back & was in a hurry to finish it, so didn't put enough quilting in it & the sheet eventually just shredded! I picked it all apart for her, fixed the places on the front that had also come apart and now it's waiting for her to put it back together again.
I agree with lfw045 too - pin baste & check the batting first, then go ahead & do what needs done. I bet it will be lovely again when you are done!