Advances in brain-machine interfaces (BMIs) have greatly enhanced the control of assistive devices like hand exoskeletons, providing new rehabilitation possibilities for individuals with impaired hand function. However, the presence of cognitive distraction during device operation may negatively affect performance. This study explores the impact of cognitive interference on a brain-controlled hand exoskeleton system. Participants were required to perform hand movement tasks using the exoskeleton while engaging in a cognitive distraction task. The results showed a significant decline in task completion rate and a marked increase in response time as cognitive distraction intensified. These findings underscore the need to mitigate cognitive distraction in brain-controlled systems to enhance performance, especially in rehabilitation contexts. This study contributes valuable insights into the interaction between cognitive distraction and brain-controlled hand exoskeleton performance, laying the groundwork for improving BMI reliability and effectiveness in practical applications.