I would first discuss the problem with the person who did the quilting.
Give her/him an opportunity to either do it over or to refund what you paid her/him.
If a "do-over" is not in the cards, and if you have not yet added the binding, the next best thing is to add a second backing yourself. Use a quick, but decorative, stitch such as Turkey Tracks to attach the second back to the quilt. As long as you take care to ensure the new stitches don't show on the front, it will look just fine. Just remember to examine it under very good light to ensure the original back fabric doesn't show through the new one.
I have had to do this on more than one of my own quilts when my freemotion stitching looks good from the front but horrid from the back.