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rule #1: be kind
The south pole doesn't move. The ice sheet moves, so every year they move the marker to keep at the actual pole.
Well that's just a matter of your inertial reference frame.
The pole is defined in reference to the earth, so the frame is fixed. The pole moves in respect to the ice sheet, sure, but that's why they have to move the marker.
The earths axis of rotation does process over time too which I think might cause a very small portion of the movement too, I'm not 100% sure though 😅
The put out a new marker with a new style each time afaik. So if you're a member of the 300 club, you can tell which year it was done by the pole marker I suppose. :)