I keep constantly raising this trait from the very beginning of the game from various card outcomes, but I've yet to see any trait check or challenge involving it. Is this trait even used for something or is it just some kind of progression meter?
Touched by Fingerwork is one of a particular set of nebulous progress qualities that relate to certain long-term mysteries of the Neath, specifically (major spoiler)
the Fingerkings, a faction of dream-snakes that "exist" only in Parabola, and which you can begin to involve yourself with in the Wars of Illusion.
Other similar qualities are Approaching the Gates of the Garden, Walking the Falling Cities, and Seeing Through the Eyes of Icarus.
These are all used to pursue particular and singular stories, though some have fewer cash-in points than others. Touched by Fingerwork is the least useful, being used only for a short one-time story to gain access to the Clay Quarters, and used repeatably in just one action that exchanges Parabola-Linen for Making Waves.
That said, there's no particular harm in letting it climb at the moment, and it is possible that, if and when Parabola opens up sometime in the future, it will become more useful.