A teleoperation system is referred to as a plant that is controlled remotely, and it is often composed of a human operator, a local master manipulator, and a remote slave manipulator, all connected by a communication network. Bilateral teleoperation systems (BTOS) include transmissions in both the forward and backward directions between the master and slave. This paper discusses a class of (BTOS) focusing on the security of the system after modeling the master and slave robots mathematically. The false data injection attack is examined, where the attacker may inject false data into the states that are being exchanged between the master and slave robots. The vulnerability of BTOS, where the attack destabilizes the system, is presented. A deep learning-based detection technique is proposed to detect the presence of false data injection attacks. The deep learning model with convolution neural network structure is trained and tested with considering complex attacks where the attacker has full knowledge of the system and proficiency to emanate and control the target system. The proposed model achieves 96\% validation accuracy, and the efficacy of the proposed deep learning detector is demonstrated and tested into the BTOS.