Well, in the end I had to use a drill and drill off the head. It was impossible to pull it out. After I removed the lid from the filter box I saw why: the thread isn't actually in the plastic of the filter box, but in a little metal oval-shaped cylinder-type thing. So I couldn't pull the screw out by stripping the threads, because those were metal too. and the screw didn't turn: it was still completely stuck in that little metal cylinder, and when I turned the screw, the cylinder would turn with it. I tried to dig it out with a screwdriver but it's impossible to get it out, so I just left it there. I refastened the other three screws and the lid still seems pretty secure on the filter box.

The filter actually looked surprisingly clean. There was a little sand and a tiny bit of leaf in the box, but hardly any, really. I vacuumed the filter and the box and figured it's still good to go for at least a couple of months.

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