I would go ahead and quilt it. Color catchers are great to use on reds. I never trust red! it bleeds, perfect name for it "red".
No peroxide on it though. I picked up Clorox in error once. luckily it was my cats cover for an ottoman she sleeps on and it was a quilt i made fitted so i could change which side was up at times. the "back" was messed up by me so i redid the corners and used the now permanent front for her. She doesn't care.
Good luck. take it slow and easy. The customer knows it is old and in bad shape. Hopefully you both will be satisfied.