i would also recommend adding quilting- without removing the existing ties-
batting that needs to be quilted every 3 1/2" is really not suitable for a tied quilt- batts that allow up to 10" between quilting lines and (generally) say ---good for tied quilts are ok to use- and even then it is recommended to have the ties in a grid about every 4". they will be fine if you simply add machine quilting to them. the ties give them a very cute look-and the quilting will ensure they hold up to being used & laundered.