I have had several people ask me about this. So, I made a video showing how to score both sides of a piece of paper or card stock with precision alignment using the laser.
After cutting and scoring the front of the card, I cut an outline of the reversed card and, set up a simple right-angle jig to make it easy to put the cut cards in the same spot in the machine. I discuss several methods for work hold-down and, how to adjust for minor errors in the setup.
I am consistently able to get hair-line alignment using this approach.
While I am using a Glowforge here, this technique is essentially the same in other laser cutters.
Glowforge Boot (for reducing tray movement)
(While this incorporates fiducial markings for a beta alignment feature you may not have (Snapmarks), we are NOT using that here. We just need a right angle piece that will stay put and, let us consistently put our cards in the same spot in the machine.)
Amazon referral links for some parts and incidentals defray IT and hosting costs for a local arts organization (Arizona Aikido).