A thrust reverser of a nacelle of a turbojet engine of an aircraft extending about a longitudinal axis and including a fixed structure and at least one door which is rotatable between a closed position and an open position and including a downstream frame spaced axially from a downstream end edge of the door by an axial clearance parallel to the longitudinal axis. The thrust reverser includes a system for diverting fluids to the exterior including at least one projection fixed onto the door or the other fixed structure and extending into the axial clearance and towards one of the fixed structure or the door, while leaving an axial gap between a free end of said projection and one of the fixed structure or the door.