If correctly programmed, the quick shifter doesn’t cause any damage to the transmission components.
Only the cut-off time needs to be programmed: this is the time interval when the engine is turned off, that the quick shifter uses to free the gearbox gears from the driving torque and allow the insertion of the higher gear.
Like any programmable device, however, if it is not programmed correctly it can generate problems: as happens, for example, with injection programmed to the wrong values.
If the engine cut-off times you use are too short, the gearbox suffers mechanical stresses due to the restoration of power before the gear is correctly engaged, which is why it is always suggested to start programming the quick shifter from very high cut-off times and then go down to the optimum value.