The best thing I ever found that is food grade de-greaser that gets the grease soot and grime is TSP (Trisodium Phospate). Best secret cleaning weapon ever! This is the good stuff they took out dishwashing and laundry detergents and why they don't work as good as they used to. I now use it to clean my coffee maker, shower heads, dishwasher, etc. This is what I used that has pulled all the creosote and soot stains out of the brickwork of my fire place to like-new when I installed an insert wood stove. I was (am) impressed! About any hardware store will carry it.
...That is if you need to.