I always have this problem with Printed Treasures labels. I peel off as much of the paper as I can without spending too much time at it. I then rinse it in a bowl of running water to eliminate excess dyes. After it is wet, I can rub off the rest of the paper easily. If there is a tiny bit of leftover paper, I just leave it in there.
I press it with a dry iron until it is dry. I press under a quarter inch edge all around. Then I spray it with basting spray to keep it in place while I hand sew it on the back.