Shower – How to seal fasteners, seams, and pipe holes in DensShield

This basin trim piece you are referring to is usually connected to the tail piece flange with a very fine thread. If has been in place for a long time, they can be difficult to remove. You will need to insert something like needle nose pliers in the top and hold the tail piece from the bottom and unscrew it. Clean out all the old plumbers putty and replace it by making a "rope" of plumbers putty in your hand, place it around the top edge of the hole in the basin, then reinstall the trim piece into the tail piece section. Tighten it so it pushes out all the excess putty, and is tight. Clean up the excess, return it to your can. Job done.

Use a masonary bit (easier to get hold of)
Put a cross of masking tape on the tile to stop the bit slipping sideways when you start
Go easy, don't put too much pressure on the bit.

Tip: try on an old bit of broken tile ( or a broken mug/teacup from goodwill) before starting on the expensive tiles.