It is good of you to try and do somehting with it to stabilize it with the backing deteriorating. That may be all that is needed and you could just do ties instead of quilting it again. Without a closer look, the age would be determined by the youngest fabric that it contains. Those colors do not speak to me as the timeframe you mentioned your GGM lived but it is hard to tell by photos. See if you can find someone local that is familiar with textiles and they can help with that.
Unfortunately probably not much monetary value but sure is nice for your family.