Kim asked in the comments on my post about the cabbage rose coaster how I finished the back. I didn't do much. I took a piece of wool 3/4" wide and stitched it by hand to the outer edge of the hooked piece, catching the outer hooked strip between each loop. Then I cut around the backing about 1/2" from the hooked edge. I tacked down the loose edge of the strip all the way around.
I used wool instead of binding tape because I wanted a soft narrow strip to bind off with. The reason for this is that I have a curvy outer edge so I needed flexibility in the binding so I wouldn't end up with a bunch of lumps all the way around.
If you really want to make it "pretty" you could take a piece of wool the shape of the coaster and tack it all the way around the back over the binding. I didn't do this, but you could.