Variable stiffness of a remote robot is crucial for a teleoperation system to deal with challenging tasks. External stiffness command interfaces have emerged as a promising solution to regulating the remote robot stiffness because of the benefits of their accuracy, ergonomics, and avoidance of the “coupling effect” that usually exists in muscle activity-based stiffness interfaces. However, the use of an external stiffness command interface requires good coordination between two limbs of an operator, which take care of the teleoperation task and the stiffness regulation task, respectively, at the same time, which is demanding for novice operators in dynamic situations necessitating agile and timely stiffness adjustments. In this paper, a new concept of Stiffness Regulation Co-pilot was proposed to facilitate the use of these interfaces. A co-pilot is a virtual agent that consists of a Stiffness Regulation Policy, which infers a reasonable stiffness regulation action from the task performance, and a feedback modality, which conveys the suggested stiffness regulation action to the operator. A preliminary user study was conducted to evaluate the efficacy of the co-pilot and the effect of different modalities of the co-pilot. The results showed that the cutaneous feedback or combined with another modality can potentially improve the task performance of the system and reduce the cognitive load of the operator compared to a teleoperation system without using the co-pilot.