The correct answer is C) flames on deck from entering the tank vent. The primary function of the screens fitted to the fuel oil tank vents is to prevent flames on deck from entering the tank vent and potentially igniting the fuel vapors inside the tank. This is a safety measure required by maritime regulations to mitigate the risk of fire or explosion. The other options are incorrect because the screens are not designed to prevent vapors from leaving the tank (A), oil from flowing out of the tank (B), or air from entering the tank (D). The main purpose is to act as a flame arrestor, not to control the flow of vapors, oil, or air.