I only clean it off the lid of my WSM if it starts flaking off onto the food. Then I wad up foil and scrub it and it comes off pretty easily.
I don't know about a UDS since I have never even seen one in real life.
Jim - Another transplanted Texan
Former KCBS CBJ
Large and Medium Big Green Eggs , Black 18.5" WSM, Blue Weber Performer - Stainless, Green Weber OTG Kettle , Brinkmann SnP Pro, and a Stainless UDS. One retired Portable Kitchen grill.
Red Thermapen, Maverick ET-732, EdgePro Apex Sharpener.
Avatar is the original 1951 Weber Kettle