Answer
Launching a probe straight backward at the same speed at which the satellite is traveling ensures that the probe's tangential speed relative to the moon is zero. It would fall vertically downward; i.e., a person on the moon would see it fall straight down.
If the probe were fired at twice the speed, it would have the correct tangential speed to orbit the moon at that distance, but would do so in the opposite direction as the satellite. They might meet, violently, after half an orbit.
