Minimally invasive procedures, such as endoscopic third ventriculostomy (ETV), benefit from the increased dexterity and safety that surgical continuum robots can bring. However, due to their natural compliance, new compatible end-effectors, such as graspers or scissors, must be developed and their actuation must be considered when developing the robotic structures in which they are housed due to the inherent coupling that will be introduced. In this paper, we integrate a tendon-driven meso-scale grasper, with a closed configuration diameter of 1.69 mm, into a 2 degree-of-freedom (DoF) tendon-driven neurosurgical robot with an outer diameter of less than 2 mm. Furthermore, the kinematics of the grasper is validated and an analysis of the coupling between the grasper and the robotic joints is conducted in order to evaluate the design performance.