Stroke often causes neuromotor disabilities, impacting index finger function in daily activities. Due to the role of repetitive, even passive, finger movements in neuromuscular re-education and spasticity control, this study aims to design a rehabilitation exoskeleton based on the pulp pinch movement. The exoskeleton uses an underactuated RML topology with a single degree of mobility, customized from 3D scans of the patient's hand. It consists of eight links, incorporating two consecutive four-bar mechanisms and the third inversion of a crank-slider. A two-stage genetic optimization was applied, first to the location of the intermediate joint between the two four-bar mechanisms and later to the remaining dimensions. A targeted genetic optimization process monitored two quality metrics: average mechanical advantage from extension to flexion, and its variability. By analyzing the relationship between these metrics and key parameters at different synthesis stages, the population evaluated is reduced by up to 96.2%, compared to previous studies for the same problem. This custom-fit exoskeleton uses a small linear actuator to deliver a stable 12.45 N force to the fingertip with near-constant mechanical advantage during flexion. It enables repetitive pulp pinch movements in a flaccid finger, improving rehabilitation consistency and facilitating home-based therapy.