To preserve the quilt where it is torn, I would probably use some lightweight fusible interfacing to reinforce it.
Straighten out the damaged part as much as you can to fill the empty area,add a little thin batting to fill in the empty area, doing this from the wrong side,lay a piece of fusible interfacing over it, protect your ironing board with pressing paper or typing paper and gently drop your iron on the interfacing, don't iron, just put it down one step at a time to hold the damaged area together.
With muslin or patchwork made from faded clothing, make a new area and stitch it over the damaged part and for your own sake, think of Grandma whenever you see this area. If you wish, you could put a new piece of cloth on the back where the interfacing is. Hand or machine stitch the repairs and hand quilt or tie the new fabric through all surfaces. That is how I would fix it. I have a quilt my grandmother made me in 1934 and I have to repair the top edge, we used it lovingly. Having it brings her back every time I see the quilt and yours will too.
Carol J.