I was setting tile last night and had to stop before the room was done. I was being diligent to make sure the edges that were adjacent to the unfinished areas were smooth but in my exhaustion I missed an edge. What is the best way to break up this cured thinset without risking the adhesion of the surrounding tiles?
Tile mortar is actually fairly soft. If you have access to a belt sander, take a coarse grit to it. Otherwise, scrape at it with a robust flat tool like a cold chisel.
If the mortar is just from the day before, it will shave right off with a margin trowel or 4 inch scraper. It hasn't reached its full strength and is over HardieBacker. HardieBacker sucks moisture out of mortar very fast if you don't dampen it first; this weakens its strength, also.