Thrust reverser comprising an improved system for deploying a membrane for sealing off the secondary flow path

A thrust reverser for an aircraft propulsion assembly, the reverser comprising a fixed structure equipped with a radially inner wall delimiting a secondary flow path of the propulsion assembly intended to be crossed by a secondary flow, the reverser also comprising a mobile structure comprising at least one mobile reverser cowl equipped with a radially inner wall contributing to the radially outer delimitation of the secondary flow path, the mobile structure being mobile relative to the fixed structure between an advanced direct-thrust position, and a retracted thrust-reversal position wherein the fixed structure and an upstream end of the retracted radially inner wall of the mobile reverser cowl reveal an air passage opening through the secondary flow path between them, the thrust reverser also comprising at least one membrane for sealing off the secondary flow path, designed to deflect at least a part of the secondary flow toward the passage opening, as well as at least one deployment connecting rod arranged in the secondary flow path and of which a first end is connected, via a connection point, to a first end of the sealing membrane, the connecting rod for deploying the membrane being designed to be moved from a first position projecting radially into the secondary flow path when the mobile structure is occupying its advanced direct-thrust position, to a second position folded down toward the downstream direction when the mobile structure is occupying its retracted thrust-reversal position, and vice versa, wherein the reverser also comprises a device for actuating the deployment connecting rod, the device connecting the radially inner wall delimiting the flow path to a second end of the deployment connecting rod opposite the first, via a first articulated connection, and in that the reverser is configured such that during an initial phase of movement of the mobile structure from its advanced direct-thrust position to its retracted thrust-reversal position, the actuating device causes said first articulated connection of the deployment connecting rod to move radially inward and/or axially upstream.