Cessna 152 instructor pilot reported a runway excursion during a training flight. Upon touchdown the student veered off the runway; the instructor took control of the aircraft; returned onto the runway; then taxied to parking.

Narrative

My student and I were doing dual flight landing on [Runway] XXR at ZZZ. On final; she was maintaining centerline up until passing aiming point (numbers); and after she passed aiming point; the aircraft yawed to the right. I was verbally instructing her use left rudder and slight aileron to maintain centerline. My hand was not on the control; because I wanted her to be independent taking controls when it comes to practicing landing. On the last lesson; there were times when she yawed to the right after aiming point; and somehow she got back to centerline and landed. So I decided to trust her controls but she couldn't manage it. It was too late to execute go around; because she touched down without getting ground effect; and flared immediately. The airplane eventually rolled over one of the runway edge lights; and I took the immediate control and get back to runway. The airplane had a light dent on the right fairing after we checked. From this lesson; I realized I should be ready [at] all times by placing my hand on the control instead of verbally instructing it. I can still trust my student but I have to keep my barrier to prevent from any incident next time.