GA7-Cougar flight instructor reported intermittent vibration in the rudder pedals during cruise flight. A post flight inspection revealed a screw was missing on the rudder.

Narrative

My student and I were conducting a commercial multi-engine training flight from ZZZ to ZZZ1; Person A was flying the plane during our training. We landed at ZZZ1 and taxied back to the beginning of the runway to take-off and practice landings in the traffic pattern. During the take-off roll; we had a complete shimmy dampener failure and aborted the take-off. We taxied to parking and alerted our maintenance team and owner of the flight school. The school has an aviation mechanic that is located at ZZZ1 and they came over to inspect and repair the shimmy dampener. The mechanic completed the repair and the plane was deemed able to return to service by the school's maintenance team. My student and I completed a thorough preflight inspection and performed a thorough runup to test the aircraft systems and we agreed that everything looked in good condition. We took off from ZZZ1 without any issues and headed south bound to head back to ZZZ and stay outside of the class C airspace of ZZZ2.Towards the end of our flight back to ZZZ; my student indicated that they sporadically felt a slight vibration in the rudder pedals. I took the controls and from time to time; felt a vibration as well. We did not lose control of the flight surfaces at any point; so as PIC I did not feel that the safety of the flight was compromised. We then proceeded to land safely without any issues. After landing; taxiing to the ramp; and parking; we performed a thorough post-flight inspection of the aircraft. We found on the rudder; that 1 of the 3 screws holding it in place (top screw) was missing. Despite this; the rudder had full capability to move left and right and operate properly. This is what my student and I believe may have caused the slight vibration sporadically during the end of our flight. The flight schools maintenance team and owners are in the process of replacing the screw.