C182 Flight Instructor with student reported noticing the engine began to make a loud noise during takeoff followed by low oil pressure display. The flight crew decided to return to the departure airport.

Narrative

This was the first training activity after this C182 was returned from maintenance. The maintenance was an oil leak from a push-rod tube. It was fixed and test flown 2 days prior with no issues.My student and I performed a thorough pre-flight and run-up before takeoff. The oil level in the C182 was at 10 qts. Run-up showed no issues and oil temperature and pressures were normal.Upon takeoff (at about 500 feet AGL); the C182 started making a whining noise that was loud enough to be heard even with noise-cancelling headsets. Upon reaching 800 feet AGL; we noticed that the oil-pressure was at or just below the green arc. We radioed ZZZ Tower indicating that we were returning for a landing and we [were] showing low oil pressure. The engine noise continued until landing. The engine; however; continued to produce normal power and respond normally to throttle and prop inputs.ZZZ Tower told us that we were cleared for a landing and that we could use any pattern work necessary. They all rolled the fire and rescue trucks. We flew a normal pattern and I (the instructor) landed the aircraft with no issues. The Tower asks us if we needed any fire or rescue services and we said no. We then taxied to parking and shut the plane down.We discussed the incident with ZZZ's rescue personnel. We did a normal post-flight inspection and found that the C182 still was showing 9.5 qts (which would be normal after an engine shutdown). The airplane is due to be looked at by a mechanic; and the aircraft has been taking off-line for any rentals until then.