Greene has been described as smart and outspoken as well as beautiful and sensual. While she enjoyed a Bohemian freedom, she was also able to move with ease in elite society, known for her exotic looks and designer wardrobe. "Just because I am a librarian," Greene reportedly announced, "doesn't mean I have to dress like one." Not only did her bearing, style, and seemingly unlimited means attract notice, but "her role at the Morgan Library placed her at the center of the art trade and her friendship was coveted by every dealer."