This paper investigates the vulnerability of bilateral teleoperation systems to perfectly undetectable False Data Injection Attacks (FDIAs). Teleoperation, one of the major applications in robotics, involves a leader manipulator operated by a human and a follower manipulator at a remote site, connected via a communication channel. While this setup enables operation in challenging environments, it also introduces cybersecurity risks, particularly in the communication link. The paper focuses on a specific class of cyberattacks: perfectly undetectable FDIAs, where attackers alter signals without leaving detectable traces at all. Compared to previous research on linear and first-order nonlinear systems, this paper examines bilateral teleoperation systems with second-order nonlinear manipulator dynamics. The paper derives mathematical conditions based on Lie Group theory that enable such attacks, demonstrating how an attacker can modify the follower manipulator's motion while the operator perceives normal operation through the leader device. This vulnerability challenges conventional detection methods based on observable changes and highlights the need for advanced security measures in teleoperation systems. To validate the theoretical results, the paper presents experimental demonstrations using a teleoperation system connecting robots in the US and Japan.