This 103 year-old lady is independent and feisty. She's wedded to her old-fashioned value system where it's not polite for a man and woman to even be alone together in a room if they're not married. Our narrator describes her as demanding and rigid but doesn't judge her at all—he's amazed that she's still around at 103.
Mrs. Croft isn't really fully sketched out as a character, but she's interesting because she represents everything that is unfamiliar and strange to our immigrant narrator. She allows us to see how he can be gracious and interested even in a totally disorienting environment.