Recent advancements in tele-operated avatars, both on-screen and robotic, have expanded opportunities for human interaction that exceed spatial and physical limitations. While numerous studies have enhanced operator control and improved the impression left on remote users, one area remains underexplored: the experience of operators during touch interactions between an avatar and a remote interlocutor. Touch interactions have become commonplace with avatars, especially those displayed on or integrated with touchscreen interfaces. Although the need for avatars to exhibit human-like touch responses has been recognized as beneficial for maintaining positive impressions on remote users, the sensations and experiences of the operators behind these avatars during such interactions remain largely uninvestigated. This study examines the sensations felt by an operator when their tele-operated avatar is touched remotely. Our findings reveal that operators can perceive a sensation of discomfort when their on-screen avatar is touched. This feeling is intensified when the touch is visualized and the avatar reacts to it. Although these autonomous responses may enhance the human-like perceptions of remote users, they might also lead to operator discomfort. This situation underscores the importance of designing avatars that address the experiences of both remote users and operators. We address this issue by proposing a tele-operated avatar system that minimizes unwarranted touch interactions from unfamiliar interlocutors based on social intimacy.