Catherine lives right in New York City and she is always available to give Myrtle Wilson an alibi for going into the city to visit her. Actually Tom Buchanan is renting an apartment in the same building to serve as a love nest for himself and Myrtle. Myrtle travels into Manhattan by train. Her husband George says that he was becoming suspicious of her frequent visits to Manhattan. Myrtle does see her sister frequently. They are having a party in Myrtle's apartment when Tom and Myrtle have a violent quarrel and he slaps her so hard he breaks her nose. Naturally there is bootleg whiskey being drunk by everyone. Nick is a reluctant guest, having been dragged there by Tom. Evidently F. Scott Fitzgerald intended a contrast between the sordid party staged by Tom and Myrtle with those lavish affairs staged by Jay Gatsby. Catherine obviously knows a lot about the relationship between Tom and Myrtle, but Nick relates that she was surprisingly quiet at the inquest.
I thought the whole tale would shortly be served up in racy pasquinade--but Catherine, who might have said anything, didn't say a word. She showed a surprising amount of character about it too--looked at the coroner with determined eyes under that corrected brow of hers, and swore that her sister had never seen Gatsby, that her sister was completely happy with her husband, that her sister had been into no mischief whatever. (Chapter 10)
Catherine may have felt it was wise to have the wealthy Tom Buchanan obligated to her. In fact, Tom may have made her generous cash payments before or after the inquest to insure her good will and bad memory.
Catherine is the sister of Myrtle Wilson. Myrtle Wilson is the wife of George Wilson. Daisy Buchanan is married to a man named Tom. Tom and Myrtle are having an affair.
Catherine is such a small character, but F. Scott Fitzgerald weaves the all the characters together. All of the characters in the story eventually wind up being to one of the main characters in some important way. The death of Myrtle ends up being a major turning point in the whole story.
Even though Catherine is not in much of the story, she is connected to the whole big picture, just by being Myrtle's sister.