Since past studies on haptic and visual communication have tended to be isolated from each other, it has remained unclear whether a touch channel can still enrich mediated communication where video and audio channels are already available. To clarify this, we analyzed remote handshaking in which a robot hand that was attached just under a videoconferencing terminal's display moved according to the opening and closing motion of a conversation partner's hand. Combining touch and video channels raises a question as to whether the partner's action of touching a haptic device should be visible to the user. If it can be invisible, the action may be unnecessary, and a unilaterally controlled device may be enough to establish an effective touch channel. Our analysis revealed that the feeling of being close to the partner can be enhanced by mutual touch in which the partner's action needs to occur but should be invisible.