How critical is it if a pebble blows into a propeller while taxiing and leaves a small abrasion in the leading edge? It wasn't noticed during flight and there was no apparent change in performance of the airplane, it was only noticed after parking. This is on a single engine piston aircraft.
This sort of FOD is often not an immediate problem, however introducing any slight knick or gouge to a propeller could be the beginning of a stress fracture. The last thing you want is a catastrophic prop failure whilst flying!
The correct course of action, much like any minor damage to the airframe, is to note it in the logs, have a mechanic look at it, and make the call if a repair is necessary.
Based on the description provided; it will have little aerodynamic (thrust, drag etc) effects, which is negligible and will not notice much in terms of performance.
small abrasion in the leading edge
After parking, maintenance guy has to check it up and take decision based on the impact, maximum allowed damage in propeller, repair availability in the current airport etc...
In case of any hesitations you should refer to the documentation of your propeller manufacturer. They contain criteria for defects, which ones can be ignored, which ones can be fixed by the aircraft owner, and which ones must be fixed by the manufacturer.
Any other action (or inaction) may cause damage to the prop, engine, and consequentially to the aircraft (be it from a crash land, or a glide land).