A 2010 survey carried out by Cure Kids found 75 per cent of New Zealanders had heard of Red Nose Day and 73 per cent believed it was run by a New Zealand charity, Mr Miles said.
Counsel for the National Sids Council of Australia Clive Elliott QC said the marks hadn't been used since Red Nose Day was stopped in New Zealand in 1998, meaning they were free for his client to use.
"It all comes down to whether there was fixed and present intention to use the mark," he said.
Mr Miles argued the trademark wasn't used because of "special circumstances" after Dr Jim Sprott claimed his research into Sudden Infant Death Syndrome (Sids) showed it was caused by toxic gases from cot mattresses, and advocated the use of a plastic mattress cover.
However, Mr Miles said interest from the public had prompted Cure Kids to relaunch the fundraiser for the 2010 year.
A social media campaign and interest from both the public and media in 2008 prompted charity bosses to look at bringing the campaign back, he said.
It spent a year working on a plan, finding backers and sponsors, and working on public relations and media campaigns in the run-up to the 2010 Red Nose Day.
Mr Elliott said Cure Kids may have had intention to use the trademark again in the future. However, that was only if they found a funder to support the day, and therefore it was not "present intention".
He said the trademark had a specification to focus on education and training when really, he argued, the day was solely focused on raising funds for children's charities.
The hearing before Justice Simon Moore will continue later in the year, with a date yet to be set.
