As the disease progressed Burton was moved from her Henderson home into the care of Hospice West Auckland, where she died last May.
But that was not where Grace's connection to the hospital ended. Four months later she was volunteering as a youth ambassador as part of Hospice West Rangatahi.
"Although there were lots of other organisations involved in my grandmother's illness, I found that hospice was the only one that I saw on a regular basis and felt like I really connected with, so I decided to volunteer there."
At her induction that connection was reaffirmed when she met a nurse who had looked after her grandmother. The nurse recounted conversations where Burton had spoken of how proud she was of Grace.
As part of the programme, youth ambassadors help out at events like Craft Out West and Polyfest and engage with the public.
"We are trying to engage other youth and trying to tell them about hospice so they know it's not just for older people because that's kind of a stigma," Grace said. "To do that, we have workshops. We had a workshop on grief. That allows us to help others, those our age, who might be having those problems."
Grace, who has won an academic scholarship to study at Lynchburg College in Virginia later in the year, said she had enjoyed working with the organisation.
"I've realised how much of an important role they play in the community. It's such a great service," she said.
"It's not just to help ill patients but it also helps the families as well - it really affects every member of that family, even close friends."
She encouraged other young people to give volunteering a go.
"You gain so much from volunteering. You gain the satisfaction of contributing meaningfully. You get to meet new people who are like-minded."
Hospice West Rangatahi co-ordinator Amy Zhou said Grace had been a pleasure to work with.
"She always has the biggest smile on her face and was always willing to give back. She would always put her hand up first."