Hmmm really hesitate to suggest this as it's not user friendly stuff at all.
You must wear rubber gloves and cover your skin (shorts are out), it will eat into metals such as aluminium etc. Just the fumes will do that so hopefully that will give you some idea of what your dealing with.
Only use it in a very well ventilated area.
It is however widely available and is commonly used for removing mortar from bricks if the brickie has been a bit messy. It disolves concrete cement and bricks. Also used in swimming pools sometimes.
Can’t guarantee it will work on your problem or for that mater actually leave any glaze on your tiles. But as a last resort……
Hydrocloric acid
it's inexpensive stuff, but it will kill your plants burn your skin and certainly hurt your pets and kids if they are exposed to it.
Hope I got my point over there
Cheers
Dave