An object with greater mass has a greater gravitational pull, and the effects of gravity decrease dramatically with distance. The Earth is much larger than the moon, so it pulls much harder. And, the atmosphere is much closer to Earth than it is to the moon. So, the moon DOES pull on and deform the atmosphere (just as it does with the water in the oceans to create the tides), but the attraction to the Earth is far too strong for the moon to have any chance at pulling the atmosphere away.
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