Does my travertine-tiled shower have thin set leaking out the bottom?
I suspect that's butyl sealant that a lazy installer used to prevent moisture from wicking up behind the tile, avoiding a trip to the hardware store. You might carefully trim it off with a razor blade and cover it with what should have been used in the first place: "tub &amp; tile caulk".

Thinset has only two consistencies: powdery when dry and concrete-like after exposure to moisture.