Start with penetrating oil and gentle pulls. If that fails, heat may be the answer. You also can try a magnet, pliers, or ...
You clean the filter with a soft, dry brush, compressed air, or rinse it with a mild detergent if it is a sponge-type filter.
If you are a regular reader, you know I am famous for reminding you to get your chores done. And I have been told it works ...