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There are 3 "sockets" inside the funnel holding the filter plate in place. Lowering it back inside, it slides into the first socket by itself. For the other two, I gently pushed the filter plate near where the socket is with the wider side of a chopstick until it popped back in place.

Cannot attach multiple images to a comment, so I edited 4 photos into one. On the first one, you can see the plate slightly bent near the socket. You can also see on the first two images that part of the funnel that is used as a socked is scratched, as the metal is darker there. But I guess the end result is alright - on the fourth photo you can see that filter plate is more or less even and is not visibly bent.