The screen in the fantastic fan comes off very easily. It's called a Pop N' Lock Screen. You can see a small area around the outer edge of the fan screen were you can grab it (a finger tab area). Then you just pull it down. There are little tabs all around the edge that keeps it in place. It looks like it is going to break but it doesn't. When we first got our 08 model I called the company and asked how to remove the screen. When the tech told me I told him I thought I would break it. He said "Go for it, if you break it I'll send you a new one for free". While I had him on the phone I did exactly what he said and it worked perfectly. As you grap and pull down on the finger tab area the little tabs that hold it in place will release one by one.
Here is a link to their site that shows you how to clean them. http://www.fantasticvent.com/faq/knowledge_base/how_to_clean/how_to_clean.html
You do not have to unscrew anything unless you have the older model but I would bet in yours you have the Pop N' Lock. Here is a link to show you exactly how to remove the screen http://www.fantasticvent.com/operating/how_to_operate_assets/pop_n_lock.pdf
Their diagram at the top of page shows the screen with screws in the figure on the left and the POP N' LOCK in the figure on the right.
We cleaned ours a few times in FL this winter. Yes, after a few weeks down there the screen really gets dusty.