Do you think the chefs at a restaurant would be mad if I ask them to clean off the grill before making my food?
They might be, why do you want them to clean the grill off before making your food?
I don't like it when my food touches older food left on the grill.
Most chefs would certainly clean the grill before preparing your food. You don't have to tell them how to cook your food.
I'm not sure, the service seems questionable here and people don't look very happy with their meals.
I think the chefs might be offended if you mention something like that to them. Trust that they'll prepare your meal in a professional way. Only mention cleaning the grill if you're worried about a food allergy.