From your photos, it appears that the holes were counter sunk, there appears to be a beveled hole that is holding the sealant. If the rail is solid fiberglass, you can use the old holes. If the rail has a wood core, then the proper way to install the teak trim is to drill oversized holes, fill with thickened epoxy, and drill new holes in the epoxy. A third option is to clean the rails and fill the holes with gelcoat and be done with finishing teak.
BTW, if you haven't done so already, cover the holes with some blue painters tape or UV resistant duct tape to keep water out of the holes.
BTW, if you haven't done so already, cover the holes with some blue painters tape or UV resistant duct tape to keep water out of the holes.