Prior to the flight, the doors were removed in order to make it easier for the passengers to board and exit the helicopter. During the safety briefing, the pilot took a headset from a pouch in the rear of the helicopter, demonstrated how to wear the headsets, and then replaced it. The pilot did not tell the passengers that the headsets needed to be replaced in the pouch after landing and before exiting the helicopter. Additionally, the pilot did not make the passengers aware of the danger associated with loose headsets in the back of the helicopter in a doors-off configuration. After the two passengers were transported to a work site location, the right rear passenger exited the helicopter and placed the headset on the hook located behind the front seats. After departing the site, about 3 to 5 minutes later while en route at an elevation of about 1,000 feet above ground level, the pilot felt something strike the helicopter. After landing and upon inspecting the helicopter, the pilot discovered that the right rear headset was missing and that the leading edge of the tail rotor had been damaged. Upon further inspection of the helicopter, the operator reported that the tail rotor drive shaft was found to be slightly egg shaped at its aft end.