An air carrier Captain reported on a visual approach; receiving an erroneous terrain alert after passing an antenna resulted in a CFFT event.

Narrative

During the descent to the AVP airport for a visual approach to runway 22; air traffic control (ATC) provided us with vectors to the final approach course and instructed us to descend to 4000 feet. Once we reported that we had the airport in sight; ATC cleared us for the visual approach. As a pilot flying (PF) I set the heading bug to the 'WEXIN' final approach fix (FAF) and adjusted the altitude to 2800 feet. While descending; at approximately 3200-3100 feet; we received a terrain alert. We suspected that the alert was triggered by a tower (antenna) with a height of 2125 feet; which we had already passed. In adherence to standard operating procedures (SOP); I disconnected the autopilot and pitched up to arrest the descent. Throughout the entire descent; we maintained visual contact with the tower and believed the alert to be erroneous. As a precaution; I halted the descent and resumed only after crossing the Final Approach Fix (FAF). We promptly informed the Tower about the alert and proceeded with the approach; following the published approach profile and the SOP procedures; without experiencing any further issues.