Georgie is a shy little girl who takes a liking to Oscar the Grouch when she visits Sesame Street. When Olivia introduced her to Oscar, he was the only one Georgie warmed up to. So much so that she wouldn't leave until Oscar promised she could come back.
Holding him to his promise (which, Oscar says, a Grouch never breaks), Georgie visits Oscar in Episode 1195. She brings him a present in the form of a potted plant. Oscar is annoyed at the presumption that he'll have to water it and watch it grow into a pretty flower. But Georgie tells him that it's done growing, and that it grew down into the dirt. As Oscar pulls it out of the pot, he's pleased to find that it's a red onion. Impressed with her display of class, he offers to make them some tea with it.
Later, after Oscar's been reading to her a variation on "Row, Row, Row Your Boat" from a collection of Mother Grouch stories, Oscar teaches Georgie how to read. Holding up some flash cards, Georgie sounds out the words that Oscar has arranged for her in a rhyme structure. Only the important words though, according to Oscar: grouch, yucchy, and rotten.
At the end of the episode, Gordon arrives to announce the sponsors. Georgie is well-informed enough by this point to identify the letter G and offer that it's the letter that starts the word Grouch (to Oscar's annoyance).
In a later episode, Oscar goes to visit Georgie at day care.