I removed the screen based upon this video (
https://www.google.com/search?q=fant...O0PEPloK8iAc38).
You do have to just pull down and it pops out (I was afraid that it would break the pins, but it was fine). I couldn't believe how dirty the screen was - and that was just after cooking in our TM maybe a dozen times!
At first, I hosed it down, but it was still a bit sticky. Then I used a sponge and soap to wash it and these little black balls of goo just started sloughing off. It was pretty gross! Then, I just put it in the sun to dry and popped it back in. Much better!
And as an added bonus, with the screen removed, I could see the model number and serial number of my fan! I have a Dometic/Fantastic Fan FA1200.