Nice barung. I was watching this one on eBay. While the coins were undoutably added at some later date i'd say that was still some time ago and i don't get the sense that they were added to give any false impression of date. Probably an authentic decoration.
As for the leather, it looks like it was added to allow someone to hang the barung on the wall. Doesn't seem to have any other practical purpose. So i'd say leave it if you are going to hang it in a similar fashion.