Thread title didn't inspire me to look originally!
Your removing remedy would have been the only suggestion I would've had to overcome the hand mark, however it highlights the importance of sealing the encaustics before they are fixed.
Being made of neat coloured cement they are extremely porous - like blotting paper - and as such dust off with a clean brush, handle on the sides, and seal. Allow to fully dry and work clean while fixing. I wouldn't recommend washing the tiles prior to sealing as uneven absorption and drying will cause the sealer to dry patchy.
Original thread title was - 'what's the easiest'