A thrust reverser for an aircraft propulsion system includes a passage, a blocker door, an actuation linkage and a damper. The thrust reverser is configured to move the blocker door from a stowed position to a deployed position using the actuation linkage. The blocker door is located radially outboard of a flowpath relative to an axis when the blocker door is in the stowed position. The blocker door is configured to redirect air flowing in the flowpath radially outward through the passage when the blocker door is in the deployed position. The actuation linkage is pivotally coupled to the blocker door at a longitudinal distal end of the actuation linkage. The damper is disposed at the longitudinal distal end of the actuation linkage. The damper is configured to engage the actuation linkage and damp vibrations in the actuation linkage. The damper is configured from or otherwise includes elastomeric material.