I run steel wool over the inside of the lid every couple of cooks. Not trying to get it really clean, but trying to get the loose bits off. If you don't clean it off at all eventually it will start flaking off and get into your food, and that is not good eats.
The hood uses a lock nut to keep from spinning loose over time so it won't be easy to remove.
Clean well and use a large Phillips screwdriver on the outside that fits correctly with a 7/16" wrench on the inside.
Cleaning the lid on the four star is no fun. Built in like mine was challenging to keep the washer nut part from falling into a crack from which there would be no hope of recovery. I'm thinking an ounce of prevention with a scrub between cooks is wonderful advice.