I remember making these years ago. I wouldn't unpick anything, but just add the new fabric over the top. If there is a backing board that covers the fabric edges, you need to remove that. You'll need to cut a fabric rectangle big enough to wrap around to the back of the frame. In the middle, cut out another rectangle, leaving enough fabric to wrap from the inside edge to the back. The inside corners will need to be snipped to wrap smoothly. Go slow, and make your snips a bit at a time to avoid snipping too far- it WILL show.