He had a reputation for being mean and demanding "tips" to the point of extortion. An explanation of his system was given by Bobby Hutcherson in an interview. He claimed Marquette told him on his first day that he was not needed and that he should "pack your things and get on out of here." This did not occur as he had been asked to play, but Marquette made Hutcherson's first night playing at the club difficult. Marquette intentionally mispronounced his name to embarrass Hutcherson and blew cigar smoke in his face to further the irritation. However once Marquette was paid his "tip" he pronounced Hutcherson's name correctly. This is said to have been a pattern for him: other musicians had similar stories of having to pay him to avoid public humiliation. Perhaps because of this, or because of the era, most musicians who knew him still referred to him as a "midget".
Little has been heard from Marquette since his Birdland days. He appeared on Late Night with David Letterman in 1985, during which he discussed his memories of being at the jazz club.