I do go over the back of my top before making the quilt sandwich. I take a wad of masking tape with me to deposit the threads on because once clipped, I want then gone. I clip any threads from sewing the seams but on frayed fabric, I carefully clip what is sticking up without pulling and leave the edge alone. Do not pull the fray threads as you clip! If your pieces are not exactly on the straight of grain you can weaken the seam.
Good luck and hopefully you can neaten it up without too much trouble. I also keep a tiny crochet hook with me as I quilt and if I see a dark stray thread, I carefully pull it out through the weave without damaging the top. Some fabrics are worse than others but I've never treated the edges with anything. You could try fray check as someone suggested but do a sample first. I don't know if it would make a tough spot to quilt through.
