re: Shower Curb - Slate Tile

You say that is the only problem area? On the outside of the curb? If so, I would probably attempt to pop that off and patch it. Don’t tell anybody I suggested that, but if there doesn’t seem to be any damage or the waterproofing doesn’t appear to be compromised, that’s what I would do first. It may turn out that a more extensive job is called for, but maybe not.