The Earth is more massive than the moon, and thus exerts a stronger gravitational pull on other objects.
Work Step by Step
To leave the Earth we must escape its gravitational well and the spaceship is being pulled “backward” for a large fraction of its trip before it starts “falling” toward the moon. On the other hand, when the spaceship leaves the moon for Earth, it more quickly reaches the point at which it is assisted by the net gravitational pull and is falling toward Earth. Less fuel is used.