I would definitely pick out the quilting and put a new backing on. I do not care for sheet backing anyway as they were usually a different thread count than the feed sack fabric. I also remember feed sack and flour sack fabric way past WWII. Good luck. A nice piece of wide domestic would make a backing more in character with the timeframe only they were not lucky enough to have wide fabric. It saves the seams and will be easier. They have it on sale at our local Hancocks from time to time. Have fun.