More fuel is required for the rocket leaving Earth.
Work Step by Step
The force provided by the rocket engines must counteract the greater gravitational attraction of the Earth the entire way, and the rocket is helped by the weaker attractive force of the moon. For the rocket heading toward Earth, the reasoning is similar. It uses less fuel because the force provided by the rocket engines only counteracts the weaker gravitational attraction of the moon the entire way, and is helped by the stronger attractive force of the Earth.