The Australian charity says it holds the registered trademark to Red Nose Day and it would confuse the public for two separate charities in the Australasian region to use it.
Sids council lawyer Clive Elliott, QC, said no evidence backed the Cure Kids claim that it had been using the trademark in the year to June 2010 as it canvassed support for, and began planning to bring back, the Red Nose Day fundraiser.
Internal use during that period did not count, he said, and because it had not succeeded in securing sponsors before that date, the trademark could not be said to have been "on the market".
The law required "public and external use directed at the outside world", he argued, which represented "the fundamental underpinnings of what's referred to as trademark use".
"What they were doing here was securing a partner to engage in fundraising activities ... so in that sense it's an entirely private matter."
It was contrary to established law to hold a trademark for years and not use it, which was classed as "covetous", Mr Elliott said.
The Sids council had begun "filling that void" in NZ, he said.
Cure Kids had "basically dropped the ball for too long and permitted someone else with a legitimate interest in Sids to support the local market".
During the first half of the hearing in September, Cure Kids claimed it had "special circumstances" which meant it was forced to suspend use of the Red Nose Day image and fundraiser event for more than a decade.
The hearing, before Justice Simon Moore, will continue today.
A nose for news
*1989 to 1997: Cure Kids runs Red Nose Day in NZ.
*2009: Charity begins work to resume campaign in 2010.
*June 29, 2010: National Sids Council of Australia applies to Intellectual Property Office of NZ (Iponz) for trademark.
*November 19, 2010: Cure Kids runs Red Nose Day.
*March 14, 2014: Iponz case is heard. It revokes the use of the Red Nose Day images and logos by Cure Kids on the grounds of non-use between May 2007 and May 2010.
*September 16, 2014: The first half of the Cure Kids appeal against the National Sids Council of Australia is heard in High Court at Auckland.
*November 24 to 25, 2014: Appeal hearing continued.