Have you ever seen the inside of a restaurant smoker or barbecue? They never clean them, maybe knock off some crude. Heat sterilizes any potential bacteria. They don't even clean the grates.
The stuff built up inside the smoker is called seasoning. Like Turbodad says, scrape off when you see flakes and use the Simple Green on the outside. Inside, my grills are the only thing that gets cleaned (and occasionally the internal probe).