The publisher's filing alleged that Netflix is benefiting from an association with the phrase, adding that Bandersnatch has been marketed and widely linked to the phrase.
"Netflix has no license or authorization to use Chooseco's trademark and, upon information and belief, used the mark willfully and intentionally to capitalize on viewers' nostalgia for the original book series", the lawsuit states.
The popular "Black Mirror: Bandersnatch" episode debuted December 28 and allows viewers to select how they want the story to go and get different endings.
"The misappropriation of our mark by Netflix presents an extreme challenge for a small independent publisher like Chooseco", said Shannon Gilligan, widow of Choose Your Own Adventure creator R.A. Montgomery, in a statement. It was one of the most popular children's series in the '80s and '90s.
Chooseco claims the "grim content" included in Black Mirror: Bandersnatch tarnishes their name and the dark themes in the film are too mature for their audience. The game is an adaptation of a "choose your own adventure book", a phrase that the main character Stefan (Fionn Whitehead) says on the show.
Chooseco added that 20th Century Fox now holds an "options contract to develop an interactive series" and that Netflix has been actively pursuing the licence since 2016.
Chooseco, which has owned the trademark since the 1980s, is claiming infringement, dilution and unfair competition and demanding at least $US25 million ($35 million) in damages or Netflix's profits, whichever is greater.
Mashable has reached out to Netflix for further comment.