A recruitment drive by the Boy Scouts of America is proving "highly damaging" to the Girl Scouts, lawyers acting for the latter organisation say.
The "infringement" meant many parents mistakenly signed their daughters up for Boy Scouts, thinking it was Girl Scouts, lawyers said.
In response, the Boy Scouts accused the Girl Scouts of starting a "ground war".
The Boy Scouts dropped the word "boy" from its recruitment programme, and opened up to female members, in 2018.
It said at the time that it was renaming the Boy Scouts programme Scouts BSA as it prepared to allow girls to join.
But the Girl Scouts said the change would erode their brand, calling the move "uniquely damaging" to them, filing an initial lawsuit in November 2018 against trademark infringement.
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Last month, lawyers acting on behalf of the Boy Scouts asked a judge to throw out the lawsuit, which suggested it could not use "scouts" or "scouting" in its recruitment material for girls.
In the latest filing at the Manhattan federal court on Christmas Eve, the Girl Scouts described the new recruitment programme as "highly damaging" to its organisation, having caused an "explosion of confusion" among parents.
"As a result of Boy Scouts' infringement... [there have been] rampant instances of confusion and mistaken instances of association between Boy Scouts and Girl Scouts," the papers stated, adding that the organisation could provide proof of such instances.
In a statement released on Saturday, the Boy Scouts said this was "not only inaccurate - with no legally admissible instance of this offered to date in the case - but it is also dismissive of the decisions of more than 120,000 girls and young women who have joined Cub Scouts or Scouts BSA".
In October 2017, the Boy Scouts' board of directors voted unanimously to open the century-old club to all children.
The move triggered a fierce backlash online, with the Girl Scouts accusing the group of initiating a "covert campaign" to recruit girls into an organisation that had a "well-documented" declining membership.
The Boy Scouts reportedly has close to 2.3 million members in the US, down by about a third since 2000, compared with about 1.7 million members for the Girl Scouts - excluding adult volunteers.