Mrs Burnie - dressed in a tank top and shorts - was in Mitre 10 Lincoln Rd in Henderson before Christmas when a man behind her in the customer-service queue pointed out her mole.
"[He] said to me, 'Excuse me, love, you know you have a black mole on your back you should be really concerned about.'
"At first, I thought he was trying to hit on me -- I thought, 'That's a nice line.'
"But then he told me his niece had passed away at the age of 25, and I realised he was very genuine and very caring.
"And so after that I made an appointment to see the doctor, and then found out that it was malignant melanoma and it was invasive."
Mrs Burnie said she thought she was going to die.
However, after having a 5cm patch of skin removed from her back, she received the news that the tests had come back clear.
"It's not travelled, which is fantastic."
The good news spurred her to reach out to the man.
"I just wanted to thank him for saving my life," she said. "The doctor told me last week that had it been another six months, the outcome would have been totally different for me.
"I said, 'I can't die, I'm far too young, and I've got a teenager, an only child. I can't.' So that was quite frightening.
"So I thought I'd just say thank you to that gentleman."
Mrs Burnie -- who describes herself as a survivor -- had previously had two non-cancerous moles removed from her back, but had not been worried about developing melanoma.
She admitted that while she ensures her teenage son wears suncream, she never uses it herself.
She has now sworn to invest in some summer T-shirts to make sure her back and shoulders are covered from the sun when she's working in the garden.
Mrs Burnie said more than 20 emails had landed in her inbox since she posted the message on community network Neighbourly.
Many asked for advice, but many others said her story had inspired them to get their moles checked too.
Her message told of the encounter at Mitre 10 Lincoln Rd and how she wanted to thank the man.
"Whoever you are that approached me -- I am a mum with a young teenage boy. THANK YOU for saving my life. I am truly appreciative of your advice. THANK YOU THANK YOU SIR whoever you are."