It took me a long time to understand what you were showing here so let me make sure I’ve got it. It seems you’re not able to reliably get back to the same physical position on the bed after making moves of the laser head.
So in your diagram you’re saying that in Pulse #1 you’ve moved first to the upper right, then came back to “center” and did a laser pulse? Then on Pulse #2 you went to the Upper Left, came back to “center” and pulsed again? And you repeated the same for #3 and #4?
And the problem you’re highlighting is that the laser doesn’t seem to be getting back to “center” especially on the Y-axis.
Can you confirm this is the situation? If not, please clarify.
If this is correct this seems like it could be an issue with backlash. Check that the pinion on the steppers are held firmly to the stepper. Recheck the grub screws there. Manually move the gantry back and forth along the y-axis. Is there a lot of “slop” before the stepper are engaged?
Another thing could be if the stepper is not staying engaged that it could be “relaxing” and losing position.
What kind of controller is this on?