Really? No oil leaks attracting grass and dirt either, all over the block and fins? Even under the air directing pan that goes around the block? Behind your muffler or any other areas?
This must be a brand new or hardly used mower. But wait, the included picture, the lower block is filthy. Don't think your comment is accurate sir. I bet a cold beer that block is grungy.
Either you don't know where or what the top engine cover is or are calling the top side of the cover grass and mice free. Look UNDER the top cover. Look for some cooling fins.