No amount of human activity, short of using some kind of superbomb or redirected asteroid to destroy it or a large part of it, will have any measurable change to the Earth-Moon relationship.
“No amount of human activity”
I believe you are wrong. Massive minning extractions from the moon over some long period of time could do it. The moon is only 1.2% of the mass of the earth yet its impact is large in many ways. Changing its mass by massive minning extractions could over time change the affect it has on the earth.