During an instructional flight, while flying on the left downwind leg of the traffic pattern at an altitude of about 1,000 ft above the ground, the flight instructor and the student pilot heard a momentary grinding noise of what sounded like "metal on metal." The flight instructor described that the noise lasted no more than 2 to 3 seconds and immediately abated. The flight instructor and student did not see anything approaching the airplane or its flight path before the noise occurred, nor did they report any sensation similar to an impact. The flight instructor and student pilot subsequently landed the airplane without issue and during a postflight inspection with the airplane’s owner, the flight instructor noted damage to the right side of the engine cowling and substantial damage to the inboard aft face of one of the propellor blades. There were no visible blood or bird remains present on the propeller or cowling. The flight instructor and airplane owner postulated that the airplane may have impacted an unmanned aerial system (UAS), and the airplane owner subsequently coordinated a ground search for debris in the days following the accident; however, no UAS components was located. Review of Federal Aviation Administration (FAA) records revealed that no Low Altitude Authorization and Notification Capability authorizations were requested for the area at the time of the accident, nor had any UAS operational waivers had been filed with the FAA for operation in the area at the time of the accident. Given all available information, the reason that the airplane’s engine cowling and propeller were damaged during the flight could not be definitively determined.