Cybersecurity in control systems has been actively discussed in recent years. In particular, networked control systems (NCSs) over the Internet are exposed to various types of cyberattacks such as false data injection attacks. This paper proposes a detection and mitigation method of the false data injection attacks in interactive NCSs, i.e., bilateral teleoperation systems. A bilateral teleoperation system exchanges position and force information through the Internet between the master and slave robots. The proposed method utilizes two redundant communication channels for both the master-to-slave and slave-to-master paths. The attacks are detected by a tamper detection observer (TDO) on each of the master and slave sides. The TDO compares the position responses of actual robots and robot models. A path selector on each side chooses the appropriate position and force responses from the responses received through the two communication channels, based on the outputs of the TDO. The proposed method is validated by simulations with attack models.