The link won't open for me, so I'm not too sure what the damage is.
Have you fixed the quilt??

Could you possibly unpick the squares as gently as possible, and cut new material, matching the exact size of the one you just cut out, and sew back together??

Jackrose has some good tips - the local quilting shops are full of the oldies who just LOVE to help when it comes to crafty projects!

HTH