Hi,
I'd recommend you bring a couple of straight edge razor blades, a #2 Philips screwdriver, a caulk gun (with built in poker), some masking tape, a plastic spoon and some GE Silicone caulk. Mine has a fiberglass piece, no teak in this area. Later models may....
The top will come off and the pole will pull straight up - no tools required. Cut the sealant around the fiberglass piece. Remove all the screws the hold the fiberglass to the cabin step. Place your hand in the table hole center and pull the piece out. Clean the edges of all surfaces using the razor blade removing all caulk. Reverse the steps for removal. Tape caulk areas and install caulk and use a finger wet spoon or finger to get the right caulk edge. Pull tape before caulk sets.
The table base is screwed but has nylock nuts on the back side. I don't think you will get these screws out without accessing the backside to hold the nuts.