Have you thought about putting the quilt label over this space? I would still 'secure' the fray area with an iron on interfacing to make sure it doesn't continue to fray.
Even if you try the other suggestions of removing the binding, using fray check or interfacing...if it doesn't look good, you could apply the label over the area with the bottom of the label right on the binding, therefore concealing (and protecting) the fray area entirely.
Good luck...let us know how you handled it.
Nan