Plumbing – Shower drain removal with no rubber gasket

It's possible the water is getting around your shower, possibly where the tile meets the tub or pan (if you have one), or behind the fixtures, or even around the door (if any).

I would check all of these and recaulk where appropriate before going in for wholesale destruction. Try splashing water by hand/bucket on areas you might suspect and see if that leads to leaks.

Or maybe you even have leaky plumbing in the wall. Do you have access to see in there?

Drain covers are specific to the tile drain manufacturer and can be difficult to find. Yours, however, looks to be of a common type and is very much like the middle one in this picture. I would take careful measurements and make a paper and crayon "rubbing" of your drain frame and go to the best plumbing supply shop in town (try a really good tile supply shop as well).

This is a website you might try: https://www.plumbingsupply.com/draincovers.html

It is odd that there are no screw holes in the drain scupper, the cut-outs in the tile frame are made to provide screw clearance. There is a chance that your tile guy tiled in a drain frame that was not the style meant for the actual drain assembly. If that is the case you may have to resort to a "snap-in" style retrofit cover. They never look as nice as the original but it's better than an open hole.