Years ago I decided I no longer wanted to clean that greasy thing so I came up with a plan, and use old pantyhose! Now, this won't work for everyone depending on the shape and size of your screen, but it's perfect for mine. The fan on our Dacor range is not an over-head fan, it is a down-draft fan. The filter is the full width of the range 36" or whatever it is and about 4" wide. I simply cut the legs off an old pair of pantyhose and slide the screen into one leg. I then stretch it tight and tie a knot on the end. When it's ready to be changed I just cut the knot and then roll the pantyhose up and toss it in the trash. I keep the extra leg handy on a towel rack under the sink for a quick replacement. It works so well, and I never have to clean the screen any more! The panty hose has all the grease, slime and dusty dirt stuck to it and my hands don't even get greasy when I remove it!
Again - big thanks to Tammara for this fabulous hint!