The solution comes down to how much thickness you have left. If you feel that you have enough material to remove the screws, deepen the countersink, rescrew and
plug, followed by a light sand and reoiling (teak sealer) then go that way. If you only have a few mm of teak left, then I'd consider removing and replacing.
I've slowly replacing mine with PlasTeak (PlasDeck) .. looks, sands, cuts, just like new teak, but doesn't
rot and doesn't get too hot from the sun. You glue it down and caulk in between the pieces - requires very little
maintenance and looks/feels just like new teak... Have a look around on Youtube, there are a few "how to" videos and you'll see how it works/looks.
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