Another way to remove the teak plugs is to drill a small hole in the center of the plug. Insert a suitable size screw into the hole. As you screw in the smaller screw it will "jack" out the plug exposing the larger screw behind the plug.
I believe this method reduces the chance of accidently enlarging the original hole. If the hole is enlarged, the new plugs won''t match the hole size and would be difficult to install properly.