Listen to George's whole sentence, "She's sticking it to me that she makes more money than me." He thinks Elaine paid for his coffee to show off how much money she makes. To use a more formal expression, he though she was "flaunting her wealth."

‘Stick it to someone’ means to deliberately hurt or embarrass someone, but usually with the idea that it’s justified, as revenge for example. It sounds old-fashioned. I neither use it nor hear it. (TV shows, of course, have to be interesting and therefore can’t have realistic dialogue!) A well-known example is: ‘Stick it to The Man’ (Urging the powerless to rise up against the powerful)

^^^ ...he thought... ^^^