I put it inside. If you have an old wet suit, it works really well too. You can even try acoustic rubber spray. It works, but I find the neoprene/mouse pad works better. Even a piece of cardboard glued in will work a little. I use wall board glue, here it is called " PL400'. It's really thick and sticky stuff, permanent too. You can use any glue that will hold up to the grease an heat though. If you can get PL400, it's never coming off, even if the Hulk smashes it.
If you use a thick piece, you will have to make a spacer/gasket to move the cover out some to prevent it from coming in contact with the drive gears and clutch plate.