First, let me explain what I observed from your picture. It appears that you did a raw edge finish. Muslin is not the best for this technique unless you are using high quality muslin like Moda or the Legacy brand from Joanns. For an item that will be washed frequently, I would fuse a light weight interfacing to the fabric first, and then iron on your fusible webbing. Then cut out your piece. This will give the fabric some extra stability and also helps to hide the fabric show-through from the main fabric.

Your zig zag stitch looks too narrow and may not have caught enough of the fabric on the applique and the background fabric. I would use a wider zig zag and shorten up the length.

Now to fix this: You can one of two things. Remove the damaged applique and replace it using your muslin, interfacing and webbing. It will take a little time to rip out and redo, but it will probably look the best.

Or, you can make another piece and cut it just a smidge larger and redo the piece by placing the new piece over the old one. Use your muslin, but reinforce it first. Interface first, add webbing, and cut out about 1/8th inch larger. Then adhere and re-stitch. This will cover the damaged piece but will also add a little more thickness.

Hope this helps. It can be fixed. It just depends on how much time your want to spend. Good luck and I hope my comments have not been too critical. I think the use of applique work on a quilt gives the work a very special touch from the heart.