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

I had a laser treatment done on my entire face in January this year with the Veris CO2 Laser. The nurse used a higher setting on my cheeks which resulted in grid-marks/squares that have become etched into my skin. What I was wondering was how these lasers work: how deeply do they penetrate the epidermis/dermis, and what other treatments (such as dermabrasion, deep chemical peels, micro-needling, radio frequency, or other lasers) can help with smoothing out this laser damage at such a deep level?