Captain reported landing gear would not retract after take off. The flight crew elected to perform an air turn back and precautionary landing at departure airport.

Narrative

Planned departure of XB:40 from ZZZZ. We arrived at the aircraft at XA:40 to a dark flight deck with only the ground service bus powered. This was the fourth flight of a three-day trip for the Captain-in-training during his first OE sequence. This was also the Captain-in-training qualification flight to/from ZZZZ. The Captain-in-training was the Pilot Flying (PF). ZZZZ had a 1000 ft. ceiling that was clear above 2000 ft. AGL. After a normal takeoff; the right seat Pilot Monitoring (PM) instructor noticed the gear was not retracting and informed the PF the gear were not coming up. Since we were climbing at the 0/Ret Minimum Maneuver speed until we were clear of terrain; we were climbing at 215 kts. We asked to level at 9;000 ft. and hold over the airfield at the ZZZZ1 VOR. It was suspected the nose gear pin had been left in and was possibly missed during the salute. I had considered running the 'Landing Gear Lever Will Not Move Up After Takeoff' QRH. However; the conditions were not met because the gear handle did move up. An attempt was unsuccessfully made to retract the gear by recycling the gear handle. The aircraft was below maximum landing weight and we had a safe landing configuration; so the decision was made to return to ZZZZ to have the suspected bypass pin removed if that was the problem. Upon returning to the gate; it was discovered the pin was not left in the nose gear and Maintenance found no faults in the gear operating system. Upon returning to the flight deck; the Instructor Pilot discovered the manual gear extension access door was ajar. The light on the aft pedestal was not illuminated during preflight and we were not aware of when that door was breached. Upon resetting the access door on the flight deck floor; the light on the aft pedestal extinguished and it was clear we had resolved the problem. An INFO-ITEM was entered into the Approved Model List and the aircraft departed and flew to ZZZ uneventfully with a 60 minute delay.OE training; hit city special qualification airfield training; terrain; weather; ATC foreign communication.Ensure the manual extension access door is firmly closed during every preflight and before takeoff.