"The tides don't pull the moon. The moon pulls the tides." Well of course, they each pull each other, in accordance with Newton's Third Law of Motion: "For every action there is an equal and opposite reaction."

But it's going to take an awfully long time for there to be any significant effect. And our contribution to that kind of thing isn't liable to be too significant. It's of a different order from the impact of humans through CO2 production by burning up the Carbon stored over millions of years in a few decades, which is what we are doing now.