Some printer geometries have a Z height bias from X,Y movements. A delta printer is an example. When probing the bed mesh, the X direction changes every other row in a zig-zag path. This can introduce errors in the Z height when probing. To eliminate this source of noise in the bed mesh, the final approach to the point to be measured should always be from the same direction. One possible way to remove this bias is after arriving at the measure point, move a set distance away from the point and back to the point. I have found that 1mm is enough on my delta printer. A parameter might be the distance to move away and back to the point. Potentially two parameters, one for X and one for Y. The sign of the distance is useful to compare the result depending on the direction of approach for troubleshooting the mechanics. On my current printer (Monoprice Delta Pro), the bed mesh looks like a washboard due to this problem and is not useful.
A slower but potentially more generally precise method would be to approach the probe point from all four directions, taking four measurements and averaging all 4. That would improve the first layer accuracy by splitting the difference from thevarios biases. That is actually what I would prefer, though not as simple as the above method.