Ii had this problem and made a top and bottom border of 8" blocks out of leftovers from the quilt. This got rid of the square so DGD knew where the top and bottom were. Then I put a 3" border around the entire quilt, black would be good here as they sometimes have grubby hands no matter how hard we try and this at least makes them not so glaring. Then the binding, always dark for kids as the chew on it, suck on it, twiddle it, etc.