Couple of ideas to consider - Carefully check the places where it has frayed. If the fabric can be gently tugged together without puckering the fabric around it = consider putting some lightweight fusible interfacing around the area on the back of the quilt. I even put fusible interfacing over the entire back of an old quilt once to give it some structural integrity. You can even use fusible if there are holes that cannot be repaired easily, and you could put an applique or two scattered around the top, covering the hole(s) as necessary. In this case, perhaps transfer a photo or two of your GG to fabric and use that as an applique. you could even applique the entire quilt to another piece of fabric, frays, holes and everything, then use the result of that as the top of your quilt, adding batting and backing as normal.