There's another thread about this subject on here somewhere. And a lot of different ideas.
What I've found to work well is a teaspoon or two of TSP in a cup of warm water on a rag.
TSP is trisodium phosphate. You can usually find it in the paint department of a hardware or "home store".
Do NOT get the all-too-common "TSP substitute". It is NOT the same. Read the label carefully, the manufacturers are sneaky with this. It would be very easy to end up with the fake stuff and not realize it until you got home due what I consider to be very misleading labels. Because TSP is a phosphate, it is a plant nutrient (good fertilizer). Thus, if it gets into waterways, it can fertilize aquatic plants and algae, contributing to algal blooms, which can be a bad thing. This is why efforts have been made to eliminate it from household cleaners and detergents. So manufacturers have had to come up with substitute formulas for their cleaning products.
But in some cases, the good old phosphate is far superior. This is one such case, for sure.
Because it is such a good grease-cutter, it will dry your skin out terribly. So use rubber gloves. And as with many products, you should avoid getting it in your eyes. Eye protection is probably a good idea.
I just toss the leftover solution out into my yard where it fertilizes my grass and bushes, so it doesn't find its way into the river here. No guilt!
A carton of TSP will last you years because you use so little, and it's fantastic for cutting grease, oil, and that tarry creosote that builds up in a smoker.
Wipe the surface down with the TSP and let it work for a little while, then hit it again, and it works very easily and well. I then wipe the surface down with plain water a couple of times to rinse off any cloudy residue.
I've also used cheap rot-gut vodka to good effect, but it evaporates too quickly.
I let my window get totally cruddy for a few years, and when I finally decided to clean it, the TSP was the winner out of everything I tried.
I do find that being able to see into the smoker is a plus for judging smoke and air flow.