Final answer:
The deviation of the tongue to one side when a stroke patient attempts to protrude it suggests damage to the neural control of the genioglossus muscle or the hypoglossal nerve that innervates it.
Step-by-step explanation:
When assessing a stroke patient who has a deviation of the tongue to one side upon protrusion, it is noteworthy that the genioglossus muscle is responsible for the protrusion of the tongue. Damage to the hypoglossal nerve, which controls the muscles of the tongue except the palatoglossus, can cause the tongue to deviate towards the damaged side. Therefore, if there is a deviation to one side, it suggests that there may be damage to the neural control of the genioglossus muscle on the same side or the hypoglossal nerve that innervates it.