Two New Hampshire fathers who were barred from school district events for wearing pink wristbands marked “XX” to represent female chromosomes insisted at a federal court hearing Thursday that they didn’t set out to harass or otherwise target a transgender soccer player at the game they attended.

But a judge hearing the case suggested the message the parents sent may matter more than their intentions.

Kyle Fellers and Anthony Foote sued the Bow school district after being banned from school grounds for wearing the wristbands at their daughters’ soccer game in September. The no-trespass orders have since expired, but a judge is deciding whether the plaintiffs should be allowed to wear the wristbands and carry signs at upcoming school events, including basketball games, swim meets and a music concert, while the case proceeds.

Testifying at Thursday’s hearing, both men said that they did not view the wristbands as a protest against Parker Tirrell, a transgender girl on the opposing team, but rather as a show of support for their daughters and their teammates. U.S. District Court Judge Steven McAuliffe questioned whether there is a meaningful distinction and whether their intentions matter.

“Sometimes the message you think you’re sending might not be the message that is being sent,” he said.

McAuliffe asked Foote whether it occurred to him that a transgender person might interpret the pink XX wristbands as an attempt to invalidate their existence.

“If he’s a trans female, pink might be a color he likes,” Foote said.

McAuliffe also noted that while both plaintiffs said they had no problem with transgender people outside the issue of sports, they repeatedly referred to the athlete in question as a boy.

“You seem to go out of your way to suggest there’s no such thing as a trans girl,” McAuliffe said. Foote disagreed, saying it was “like learning a new language” to refer to transgender people.

In a separate courtroom earlier Thursday, another judge held a hearing on a lawsuit brought by Parker Tirrell and another student challenging the state law that bans transgender athletes in grades 5 to 12 from teams that align with their gender identity. It requires schools to designate all teams as either girls, boys or coed, with eligibility determined based on students’ birth certificates “or other evidence.”

U.S. District Court Chief Judge Landya McCafferty ruled earlier this year that the teens can try out for and play on girls school sports teams. The order only applies to those two individuals for now as they seek to overturn the Fairness in Women’s Sports Act on behalf of all transgender girl students in New Hampshire.

Lawyers for the teens said in court Thursday they hoped the matter could go to trial and be resolved before the start of the next school year in September. They said the teens’ school districts and others in the state have asked for guidance regarding the statute. Lawyers for the state said they needed more time to prepare.

Judge Talesha Saint-Marc suggested the timing of the trial was ambitious and asked that both sides talk further about scheduling. Gov. Chris Sununu, who signed the Fairness in Women’s Sports Act into law in July, has said it “ensures fairness and safety in women’s sports by maintaining integrity and competitive balance in athletic competitions.” About half of states have adopted similar measures.