Motor recovery of the upper limb is a priority in the neurorehabilitation of stroke patients. Advances in the brain-computer interface (BCI) technology have significantly improved the quality of rehabilitation. The aim of this study was to explore the factors affecting the recovery of the upper limb in stroke patients undergoing BCI-based rehabilitation with the robotic hand. The study recruited 24 patients (14 men and 10 women) aged 51 to 62 years with a solitary supratentorial stroke lesion. The lesion was left-hemispheric in 11 (45.6%) patients and right-hemispheric in 13 (54.4%) patients. Time elapsed from stroke was 4.0 months (3.0; 12.0). The median MoCa score was 25.0 (23.0; 27.0). The rehabilitation course consisted of 9.5 sessions (8.0; 10.0). We established a significant moderate correlation between motor imagery performance (the MIQ-RS score) and the efficacy of patient-BCI interaction. Patients with high MIQ-RS scores (47.5 (32.0; 54.0) achieved a better control of the BCI-driven hand exoskeleton (63.0 (54.0; 67.0), R = 0.67; p < 0.05). Recovery dynamics were more pronounced in patients with high MIQ-RS scores: the median score on the Fugl-Meyer Assessment scale was 14 (8.0; 16.0) points vs 10 (6.0; 13.0) points in patients with low MIQ-RS scores. However, the difference was not significant. Thus, we established a correlation between a patient’s ability for motor imagery (MIQ-RS) and the efficacy of patient-BCI interaction. A larger patient sample might be necessary to assess the effect of these factors on motor recovery dynamics.