The deal includes back-pay from July 2005. In Ms Rae's case, her family estimate it amounts to at least $2000.
Her mother, Iris, has called on the IHC to show compassion after it repeatedly told her nothing could be done because no claim was lodged before September 2 last year.
"I know it's not a huge amount compared to what others will be claiming for. But her son really could do with this money. It's what she was entitled to. She worked those hours."
Natalie's son Braden, now 8, is cared for by her sister Selina, a solo mother with her own 6-year-old daughter to support.
Mrs Rae said she and her husband often helped out looking after their extended family, and the IHC money would ease bone-thin budgets.
"[Selina's] trying to run that household on her own now, with the two children. It's getting tight for her. She's trying to keep a fulltime job going," Mrs Rae said.
Braden was 6 years old when he saw his mother die a day after she was sent home following surgery at Middlemore Hospital.
"He's been so affected by it," Mrs Rae said. " We still struggle with him now, where he is petrified to leave Selina ... It's just been a nightmare for the whole family.
Mrs Rae said that after Natalie died, she phoned the IHC and was assured she would be contacted when claims could be lodged.
But David Timms, IHC general manager of HR and training, said in a statement that the application deadline was final.
"We are aware that this process has been hard for a lot of people and we have had a number of people asking us to reconsider."
Mr Timms said there were two clear criteria for settling claims - an application had to be lodged by September 2, 2011, or claimants had to be an employee on that date.
Service Workers Union secretary John Ryall said he presumed the strictness around the application date was intended to limit the Government's liability.
"The Government guaranteed the cost of the phase-in of the minimum wage, which is worth about $47.5 million a year. And then they met half the cost of the back-pay," he said.
The union filed claims for consenting union members, but records indicated Ms Rae was not part of the union.
"There was a number of non-union people who did it through lawyers ... We did talk to IHC afterwards about people who hadn't filed. But the only area we made progress on was current staff," Mr Ryall said.
The union eventually won the settlement after it lodged an Employment Relations Authority claim for the minimum wage for sleepover workers in 2007.
The authority upheld the claim in 2008, but the IHC's service arm Idea Services appealed all the way to the Court of Appeal, which upheld it again in February last year.
Idea Services appealed again to the Supreme Court, but also opened negotiations with the union which led to the settlement.