What would be the best method to remove that ugly tape without damaging the back of the bow?
it doesn't really matter what it looks like. it only matters what it shoots like
but if you simply must remove it, just sand it off with a rasp and hit it with sand paper until it's clean again. you're working with a milled piece of lumber so you'll just be taking it back to a milled state on the back surface.
silk is really cheap and an easy way to obtain some is by dropping 5 bucks for a strip from the local fabric store. just ask the personnel for the 100% silk. if you get it in white or yellow, it all but disappears when applied with titebond 3 and you'll end up being able to clearly see the wood grain.
the silk fabric bolts are ~40" wide, so i only ask for about a 6" strip. unfold and cut that in half and you end up with two 3"x40" silk strips that you seam at the handle.