Wow Henry, what a treasure! I must say I envy those who have pieces of their history like this. Your grandfather did good work.
If you want to keep the integrity of the quilt, you will need to find some red fabric from the same era as the quilt. The best way I've seen to 'fix' areas where fabric has ripped or is breaking down is to simply applique the new fabric over the old. I have not tried this technique though I do have a quilt given to me by an old family friend and this is the technique I am going to use to restore it. There are other techniques out there that might suit you better. I don't know enough about them to go into any detail. Hopefully someone else who does will post. I hope this helps.
~Tiffany