The point that gravity from the moon has a similar effect as gravity from the earth is about 80% of the way to the moon. This means that if something is 79% of the way to the moon and stationary, it will fall towards the earth.
Atmosphere is pretty much 1% to the moon or less (if you don’t count the exosphere, it’s only .2%). If any is escaping earth’s gravity, it’s not because of the moon.
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