I would also cut the butterflies out and appliqué them to new old looking fabric.

I think I would try to unstitch each butterfly and restitch them to fabric similar to that previously used. It looks like a blanket stitch used.

I was thinking appliques too; smaller butterflies and some small flowers along with the bees and hive. Be sure to show us the end result. You can do this.

The damaged fabric looks too fragile to salvage. I too agree that the butterflies should be very carefully cut out and re-appliqued to new vintage looking squares. To me those would be the most precious parts to preserve. The addition of a label giving tribute to Grandma would also be nice.

If it were me, and for the sentimental value. I would take off all the sashing. Then carefully iron the butterflys out. Then, I would stabilize the Fabric the butterflys are on with a medium weight stabilizer. I would then, put on a new borders in the color that matches the original color. And, then have it quilted. Even with all the age and wear, it will be a beautiful quilt. And, a beautiful memory of your DGM.

I would do this approach. Find a fabric with flowers or bees or birds and cover the bad spots with the Applique. Then Quilt it with the tulle over it.

grandmothers quilt preserving
 

At a family reunion we we were given a block of my grandmother's and were told we could preserve them any way we wanted. Some mounted and framed. I'm not sure what others have done. I would tug on one of the blocks that is damaged to see if the fabric is intact before I did too much.

How about
1. a scattering of mini butterflies to cover the holes OR
2. Redo the stashing and appliqué butterflies, flowers or dragonflies over the holes on the white. OR
3. Cut out the butterflies and appliqué them on new backing, new smashing, etc

Whatever you do I bet it turns out beautiful.

I agree. It looks to me like the quilt top was folded up for storage and those darn (and I really would use a worse word than that!) varments chewed away right on the folds. That is why the holes are lined up like they are. Don't ask me how I know so well what damage from mice looks like. You would think someone with as many cats as I do would have no experience with that. But I keep my sewing rooms shut off from the cats and rooms that don't get frequented every day in a 100 year old house, well, mice find a way. Can't stand the little beasties.

Anyway, if Prism and I are correct in our assumption of mouse damage, that may be good news. The fabric may not be as fragile as everyone is assuming. I would swap out the damaged sashing pieces with a blue as close as I could get. The butterfly blocks you have a few choices. I think I would put them on to another piece of muslin (the whole block). And reinforce the hole area with either quilting or maybe a fusible in between the original background and the new backing. Then sandwich and quilt it. You could also just cut out the butterfly from the worst damaged blocks and re-applique them on to new background fabric.

another option is how many family members would want a piece of grandma's quilt? If many, maybe just cut it apart and quilt each block as a gift for each member sacrificing the worst chewed ones.

I have not conserved/repaired any quilts, but I would agree with Judith 1005: I would back the butterfly blocks with a lightweight iron-on fusible. I would also remake the sashing. There are plenty of quality solid fabrics now that you could match the colors fairly closely. Regarding finishing the quilt, I am not sure I would. I think I'd leave it as just a top and enjoy it as a family heirloom. Just my opinion.