No need to clean the coil! The portion of the heating element that gets red hot inside of the cook box burns off grease and debris naturally.
For the heat shield or bowl liner remove excess grease by simply scraping the liner with a plastic scraper.
For a more thorough cleaning, remove the liner by carefully tilting the heating element slightly upward and slide the bowl liner out and away from the grill. Scrape the grease from the bowl liner with a plastic scraper, wash with warm soapy water and then rinse. Be sure the bowl liner is completely dry before replacing into the grill. Check for grease build-up after each use.