DIAGNOSIS The grease and food splatter on the heating element and surrounding metal shield is normal, but it will smoke and smell if you don't clean it. Yeah, it's a pain, but it's necessary.
FIX Unplug everything and let the lid cool completely. The metal cap around the heating element is removable. Push up on the little metal tab inside the cap and turn it counterclockwise—it should come off. Soak that cap and the removable inner basket/rack in hot, soapy water. For the actual heating element inside the lid, wipe it gently with a damp, soapy cloth or sponge. Do NOT immerse the lid in water. Dry all parts thoroughly before reassembling.
IF THAT DIDN'T WORK For baked-on grease, make a paste of baking soda and water, apply it to the greasy areas on the removable metal cap, let it sit for 15 minutes, then scrub with a non-abrasive sponge.
HEADS UP That metal cap must be completely dry and correctly locked back on (turn clockwise until it clicks) before you use the lid again. If it's loose, it could be a safety hazard.