A Flight Instructor reported their student lost control of the aircraft during landing roll resulting in a runway excursion.

Narrative

This flight was the second flight teaching a student pilot landings. The student had been performing well; and during what was planned as a touch and go landing; my student was applying the appropriate crosswind correction on final all the way to the runway; raising my confidence in their performance. The wind for the runway in use was about a 10 knot crosswind. During the flare and touchdown sequence; my student removed all rudder crosswind correction; and the aircraft veered to the left while I took control to reapply the corrective crosswind inputs. The aircraft's left tire momentarily ran into the grass aside the runway. No runway lights where hit; no injuries occurred; and no damage to the aircraft occurred. I exited on the nearest taxiway and assessed the aircraft and situation. I elected to return to the ramp where I inspected the aircraft to verify no damage had occurred. To mitigate the risk of this event happening again; I conducted more ground instruction with my student on the aerodynamics and physics involved in a crosswind landing; and emphasized the importance of not releasing the crosswind inputs while the aircraft is in motion; even if it is on the ground.The primary issue was the student's abrupt withdrawal of crosswind corrections on landing; which resulted in a momentary; partial runway excursion; where no damage occurred to aircraft or property.