someone on here the other day removed a piece from the center of her quilt and replaced it. I am going to see if I can find the post!
ETA: I can't find the post but what she did was picked out the stitching in the offended piece then replaced it. I think in that case the block was just upside down so she just turned it around so it was right. However in your case just cut another piece of fabric exactly the size needed and sew the seams in order that they were put together in the first place. You shouldn't have any trouble.
I myself am a little crazy and an unintentional/added out of need applique would drive me nuts. Therefore I myself would take the extra time to remove the piece and replace it. However I understand others aren't as nuts as myself!