It's an obi ami. They aren't intended to be taken out and cleaned. I've found them in a lot of cheaper Tokoname ware.
Personally, I don't like them, but thats just because I prefer a sasame (clay mesh screen) If you go to Rishi's website and check out their tokoname teapots, they have some good pictures where you can see the difference (you can also see the difference in price).
Functionally, obi ami are great. They get the job done, strain out even the tiny particles, and are no muss no fuss. Just rince the pot with water when you're done.
Go here for a good review of a teapot using an obi ami filter.