Teleoperated medical technologies are a fundamental part of the healthcare system. From telemedicine to remote surgery, they allow remote diagnosis and treatment. However, the absence of any interface able to effectively reproduce the sense of touch and interaction with the patient prevents the implementation of teleoperated systems for primary care examinations, such as palpation. In this paper, we propose the first reported case of a soft robotic bilateral physical twin for remote palpation. By creating an entirely soft interface that can be used both to control the robot and receive feedback, the proposed device allows the user to achieve remote palpation by simply palpating the soft physical twin. This is achieved through a compact design showcasing 9 pneumatic chambers and exploiting multi-silicone casting to minimize cross-noise and allow teleoperation. A comparative study has been run against a traditional setup, and both the control and feedback of the physical twin are carefully analyzed. Despite distributed tactile feedback not achieving the same performance as the visual map, the soft control and visual feedback combination showcases a 5.1% higher accuracy. Moreover, the bilateral soft physical twin results always in a less invasive procedure, with 41% lower mechanical work exchanged with the remote phantom.