Donna Gianell was removed from the jury by US judge Jed Rakoff on the request of lawyers working on behalf of Citigroup.
Ted Wells, a lawyer for the investment bank, played the court a video clip of a 2009 film by Moore entitled Capitalism; A Love Story.
The film was a documentary about the financial crisis of 2008 and Ms Gianell was among a number of individuals who received âspecial thanksâ for their contribution in its credits.
Although Ms Gianellâs contribution to the film has not been confirmed, she was asked to leave the jury at the end of the dayâs hearing.
The juror was also believed to have been overheard discussing the case with other jurors, which is strictly forbidden by court rules, reports also claimed.
British firm Terra Firma launched an action against Citigroup after it claimed it was misled by the bank when looking to acquire music firm EMI.
The firm alleged that David Wormsley, an advisor from Citi, informed Terra Firm founder Guy Hands that Cerberus, a rival private equity company, was looking to file a rival bid when this was not in fact the case.
Citigroup has denied the allegations.
By Jim Ottewill