A thrust reverser for an aircraft propulsion unit, the reverser comprising a fixed structure equipped with a radially internal delimiting wall of a secondary flow path of the propulsion unit through which a secondary flow is intended to pass, the reverser also comprising a movable structure comprising at least one reverser cover equipped with a radially external wall and a radially internal wall forming a radially external delimitation of the secondary flow path, the movable structure being movable in translation with respect to the fixed structure along a longitudinal central axis of the reverser, between a forward direct-thrust position and a retracted reverse-thrust position, the reverser also including a deflection cascade and a sealing membrane to deflect at least one portion of the secondary flow toward the deflection cascade when the movable structure is in the retracted reverse-thrust position, the reverser also including a rear cascade support frame for supporting the deflection cascade,
- wherein the reverser includes an interface device between the sealing membrane and a rear cascade structure comprising the rear cascade support frame, the vanes located furthest back on the deflection cascade, and a bearing member via which the cascade bears against the rear cascade support frame, the bearing member projecting behind the vanes located furthest back and also being fastened to the rear cascade support frame,
- in that a first end of the sealing membrane is fastened to the interface device via first coupling means,
- and wherein the interface device forms an elastic clip mounted around the rear structure, and a rear clip portion of the elastic clip is arranged behind the rear structure.