In an interventional medical system, a delivery catheter for deploying a medical device of the system has a tethering assembly that includes a tether line, a grip member, and a release member, wherein the tether line extends through a longitudinal lumen of a base of the release member and is coupled to a base of the grip member, and the release member has legs extending though apertures formed through the base of the grip member. The device may be tethered to the catheter such that a proximal end of the device is held within a cavity defined by a plurality of elastic fingers of the grip member that extend distally from the base thereof; and the device may be deployed from the catheter by moving the legs of the release member within the grip member cavity to push the proximal end of the device out from the cavity.