Grumman AA5B instructor pilot reported the student lost directional control on takeoff and after the reporter took the controls the aircraft sustained minor damage from contact with berms adjacent to the runway.

Narrative

Student was demonstrating a soft field takeoff Runway XX. Winds 210 at 8 KTS. Aircraft started to drift left. Instructor (me) requested more right rudder. I applied right rudder to avoid departing the runway to the left at the same time the student applied aggressive right rudder. The combination caused the aircraft to veer right. I stated my aircraft and made rudder inputs to aim the aircraft nose towards the centerline. I could not prevent the aircraft from leaving the paved runway. I leveled the wings and determined that it would be safer to take the aircraft flying. I ensured full power and lowered the nose to a normal takeoff attitude. The wings contacted some raised berms as the aircraft lifted off. I returned to the field and performed a soft field landing to put less stress on the gear. After landing the aircraft flew fine so I taxied to the hangar and asked a gentleman that approached to alert the FBO to perform a safety check of the runway. The aircraft has some minor scrapes. I am moving soft and short field takeoffs to much later in my flying curriculum. My brief covered relinquishing controls; which the student did; however; I believe that the student didn't clear the rudders completely. I will stress clearing all controls. I will also put more emphasis on less aggressive control inputs with the Grumman Tiger due to the free caster nose wheel. As an instructor; I will tighten my parameters during takeoff.