@SanderLPFRG in the following I will assume that the engraving was done using back and forth scanning in the X direction, so adjust axis names appropriately if not.
Measure the X offset between adjacent lines in that engraving. Then try jogging the X axis back and forth a distance smaller than that and see if the tool head moves as expected.
Alternatively: construct a GCode file to engrave a short line in the Y direction, then move X a short distance (less than or equal to the offset), then engrave another short Y line, then move X back to the original position and engrave another Y line. Check that the X offset of the middle Y line from the outer two Y lines is the correct amount.
Another possibility is that the tool head is rotating about the Y axis as the belt or leadscrew pulls/pushes it first one way and then the other way. Such a rotation will affect the X position of the laser spot on the workpiece.