OK, I'm no astrophysicist, but why would any object orbiting the earth (even "high orbit") then be attracted to the gravity of the moon?
Seems like earth's gravity would not let go of such an object.
Sounds nuts.
Proximity...............
If the orbit is higher than the first Lagrange point, the lunar gravity dominates earth’s gravity and the rocket will be pulled toward the moon. Gravity depends on the inverse square of distance, so a smaller body can gravitationally dominate a larger one in regions close to the smaller body. You see this happen every time you drop something; you just don’t normally think in those terms. If you drop a ball, that ball is actually in high orbit around the sun. It doesn’t have to break free from the sun’s gravity (and indeed it does not) in order to be pulled away from the sun toward the earth. In like manner, this rocket is still within the earth’s gravity well (as is the moon itself) but is attracted away from the earth by the moon.