this is what i would do :)

I would remove that section of binding and replace it. I am too OCD to do anything else. It's too bad that happened.
Sue

You could cut a small piece of fusible interfacing,, preferably a circle so not sharp points will show. Press on where the nip is and then I use fray check on the right side to keep it from fraying. If you use a very light weight fusible, I think you can work with it. I use this to fix holes in knit shirts that are well loved to let them last a little longer.

I would replace the section(s) with new binding. All the work put into a quilt (esp. a gift) deserves a quality finish!

Thanks for the advice. I was looking for the cheater"s way out. Unfortunately (?)these are on the edge and are very small. This is a binding where I brought the backing fabric over to the front to use as binding. Was just thinking maybe I could rip out that portion and refold to put small overlay on the back over the cut and then make the folded binding not as thick in that area. I will play with this a little and let you know how I did . This is for a table runner so it will not get as much use as a quilt but fixs may be more noticible.

I used FrayBlock by June Taylor. Gave quilt away, don't know if it held forever, but looked good when I washed it before sending. Drys soft.