Oh, no! Not #461! Many quilt backs are pieced. Here are some examples:
http://www.quiltingboard.com/picture...s-t148395.html
I would just unpick enough where you can machine sew an additional strip to make the backing complete. It doesn't need to match the current backing (looks like minkee?) If you have any of the fabric used in the top, that would be great, but not necessary. you could incorporate the label if you want.
You did a wonderful job on your 3rd quilt!