The movie cast Gaga as Patrizia Reggiani who served eighteen years behind bars for arranging to have her ex-husband Maurizio Gucci killed by a hitman.
In a statement, the Gucci family claimed film producers did not consult them before allegedly describing members of the family as “thugs who were ignorant and insensitive to the world around them”.
The letter stated: “This is extremely painful from a human point of view and an insult to the legacy on which the brand is built today.”
It added: “The Gucci family lives by honouring the work of its predecessors, the memory of whom does not deserve to be upset merely to put on a fictional show that does not do justice to its protagonists.”
The family said it was particularly upset by the portrayal of Ms Reggiani who is allegedly painted as “a victim” in a “chauvinistic corporate culture”.
It comes as Ms Reggiani has said she is pleased with Gaga’s portrayal of her but added she was annoyed Gaga had not met her before filming.
The film – which premiered in the UK on November 9 – also features Al Pacino, Jeremy Irons and Salma Hayek.
Director Ridley Scott has previously dismissed family members’ criticism of the film after Maurizio Gucci’s second cousin Patrizia Gucci said he was “stealing the identity of a family to make a profit”.
But Scott told BBC Radio 4’s Today programme last week: “I don’t engage with that. You have to remember that one Gucci was murdered and another went to jail for tax evasion, so you can’t be talking to me about making a profit.
“As soon as you do that you become part of the public domain.”
The film, which is yet to be released in Italy, is based on the 2001 book The House of Gucci: A Sensational Story of Murder, Madness, Glamour and Greed by Sara Gay Forden.
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