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*Frog Dissection Ahead*
Gezhe is a joke. It's a term whose definition changes depending on the context and who's using it. It generally means OG Lubavitcher from specific Chassidic towns. It's not something 99.9% of Lubavitchers take seriously. The most common current usage, outside of jokes, is when relative newcomers think they aren't getting a seat at the table because the "gezhe" are Deep State and control the game. You're getting a peak at 50 years of gezhe jokes.