since it is just a tied cover I would redo it....IF the rest of the fabric are not dry rotted. You will need to do a stress test on the other fabrics or you might end up replacing more fabric than you thought...and if you are not using vintage fabrics, then the quilt will look "off"...
here is another thought...are the damaged squares all on the outer edges? If so, then perhaps you can trim the quilt off, leave the batting, backing etc...put in a NEW batting, then a new backing and get it quilted like that..another words, LEAVE the old quilt as it, just make it smaller!