I'd definitely envisioned some way to remove the graffiti.
If this "mine-sign" was actually carved
in a mine--that is, among stone set to be quarried--then sooner or later, each graffito is going to be removed right along with the wall itself. But in the case of writings scrawled upon more finished surfaces, then yes, re-smoothing it seems the most likely way.
The problem would be how the dwarves
feel about erasing someone else's work, and how serious that work is. If it's just some vulgar doodle, or poor scrawl reading "Ingish Dustbeam sucks sewer brew", then the cleanup worker will just laugh it off, smooth it off, and go about their day. But if it's a well-executed sign of protest, like an engraving of dwarves sleeping on the ground, then the dwarves might very well
refuse to remove it until the grievance is dealt with--
e.g., by finally giving Rakust Hametower her own bedroom, or making more mugs, etc.
But if, as Narrrz mentioned, these symbols are imbued with magical power, that's a whole different can of worms. Defacing them might invoke a curse or have various other effects, and appeasing the maker might be similarly more complicated. But that would raise another problem: If every random Urist McDorf has the mystical power to call down blood curses and whatnot, what the hell are they doing dying to goblins and badgers?