I want to know how CO2 lasers work to penetrate the skin so I can go about choosing treatment to alleviate laser damage (Photo)

you likely need nonablative fractional laser or radiofreuqency or microneedling with PRP or both to help repair this. I suggest only going to a board certified medical doctor who specializes in lasers for your laser care.  Best, Dr. Emer.

Performed properly CO2 laser should not leave grid marks or any other the of pattern. This can be a problem when pattern generators that control the laser's beam are used. The visible pattern you have are due to either excessive overlap of the pattern creating over treated areas at the edges or skip areas between grids creating undertreated areas at the edges.  At six month's it's probably not going to resolve spontaneously. The best option is to retreat using a modality that's going to treat into the dermis and stimulate new dermis like the CO2. The CO2 without the pattern generator and do freehand treating to create irregular edges rather than straight lines to blend these areas in and traditional dermabrasion would be best.