What I have read from others here is that you get a block of wood to press against the damper to hold it tightly down, right near the plastic piece. Then, "just lift up" on the plastic piece.
Do this even for newer ones that bolt on to the kettle lid, because that damper isn't flat, and you'll wind up flattening it if you take the whole thing off and use the floor to press against it.
Installation should just be a press fit back onto any other damper's tab.