Generally you would do a 2-stage jigging process where you cut the straight edge with the laser, remove the jig waste, insert your real material, then turn off the jig lines and do the rest of your work.
It’s been documents a few different ways, we all sort of arrived at similar workflows. Search for “jigging” or “jig” on the forums, there are a number of posts.
Here’s one I wrote:
https://community.glowforge.com/t/alignment-of-irregular-objects-coasters/16116