I have never used a leather butt cover. I have used an elastic butt cover/ammo holder. I didn't remove it for quite a while after I installed it. When I did remove it, there were a bunch of sticks and dirt under the cover. I would take the cover off after every few hunting trips to make sure there is no nasty stuff under there. I was lucky! Old English scratch remover got all the scratches off my gun.
Speaking of luck. I create my own luck when removing scratches. When I get a new gun with a wood stock the first thing I do is wipe the stock down with Old English scratch remover for light colored wood. Since the oil has already pigmented the entire stock when I do scratch the stock one or two light applications covers any scratches on my wood stocks. I have several guns that are over 40 years old. The wood stocks all look like new due to Old English scratch remover.