Flight Instructor on training flight with student reported aircraft elevator trim system malfunctioning. Flight crew returned to land safely.

Narrative

During the interior preflight I noticed there was an abnormal amount of nose down trim. I thought it was strange; but we had spoken to previous crew and they never mentioned it/wrote up the plane so I figured they just forgot to retrim the aircraft during the after landing checklist. I retrimmed it to slightly aft of neutral. During the climb; my Student had to add nose down trim and told me there was something wrong with the trim so we let tower know and we stayed in the pattern and landed. We were in the downwind at 2200 RPM; 100 knots; full nose down trim and the aircraft still wanted to climb. The aircraft is the aircraft that was damaged after it went off of a runway a month ago and it had recently came out of maintenance so I believe that was a contributing factor. Also; the previous crew seemed to be aware of the issue based on all the nose down trim I saw during out interior preflight so they should've filed a discrepancy form after their flight. There's a few things that we all could've done differently- 1. I'm assuming it should've been caught on the maintenance flight or a previous flight. 2. Previous crew should've written it up/warned us. 3. I should've inspected the trim tab more closely after noticing the abnormal nose down trim during preflight and/or called maintenance to check it out.