Flight Instructor reported a student lost control during landing resulting in a runway excursion.

Narrative

The airplane was established in the landing configuration on the final approach with full flaps; and the before-landing checklist was completed. The student pilot was on the flight controls; attempting a short field landing on Runway XXL at ZZZ. The airplane crossed the threshold at approximately 80 feet AGL with an airspeed of 65 knots and touched down about 100 feet past the thousand-foot marker. Upon touchdown; slightly to the left of the runway; the student pilot reduced the wind correction and attempted to stop the aircraft by applying the brakes while trying to maintain the runway centerline using the right rudder. The aircraft began drifting to the right side of the runway. The student attempted to correct by applying left rudder to regain the centerline; at this point a tire noise was heard; caused by the tires skidding on the pavement. The instructor pilot immediately took over the flight controls and attempted to correct the airplane's drift. Rudder inputs were applied in an attempt to return to the runway centerline. However; the aircraft continued to drift and eventually exited the runway; turning 180 degrees around facing the approach end on Runway XXL. The aircraft came to a rest in the grass on the left side of the Runway XXL between [Taxiways] 1 and 2. The airplane was in a level position; with the right main landing gear and the nose landing gear in the grass; while the left main landing gear remained on the left edge of Runway XXL. After confirming that all occupants and the aircraft were safe; the instructor pilot successfully exited the runway. Once past the [Taxiway] 2 hold-short line; the instructor pilot contacted ATC for taxi instructions to the run-up area of XXL for a further exterior inspection of the aircraft.The aircraft was brought to a complete stop in the run-up area of XXL; where shutdown procedures were performed. The instructor pilot conducted a visual inspection of the airplane and found no visible damage. Airport operations personnel approached the aircraft for further inspection and confirmed that no damage was observed to the airport environment; runway; lights; or the aircraft.The airplane's engine was started again for a run-up performance check; which showed no noticeable deviations from standard. After confirming the aircraft was in safe condition; the instructor pilot requested taxi instructions from ATC to return to the FBO ramp. Instructions were given to taxi via 3-4 and hold short of Runway XXR. Clearance was then granted to cross Runway XXR and taxi via [taxiways] 5; 6; and 7 to the FBO ramp. After completing the shutdown procedures; the instructor pilot conducted another visual inspection of the airplane; again finding no noticeable damage. The instructor pilot then spoke with maintenance personnel; explaining the situation and requested a more in-depth inspection of the aircraft to ensure its airworthiness and safety.