Astrophysicist here: This is caused by the moon developing a crescent shape at each end of the path, resulting in a boomerang-like behavior where the rotational velocity of the moon causes it to return back to where it was thrown.
It's beautiful, but unfortunately a fake. This is from a reddit comment for years ago:
This is supposed to represent a lunar analemma, but it's completely faked. And not just in the sense that it's a composite, in the sense that the relative sizes and positions are completely made up.
No, it actually just appears back on the left side of the path again. No one can explain why, but it almost killed the Apollo guys. Had they been there one day later…
Of course they had to go at an almost full moon. Not much to land on, otherwise.
Not taking into account movement forward/backward, and with an admittedly very crude measurement method, the total path is roughly 174,875 km. If you took a 7.4 hr flight every day for 28 days straight*, you could possibly beat the moon. Probably give a Taylor Swift a run for her money, too.
*If you only did "work days", you'd have to fly 10.3 hours a day.