Wood's mother Susan Fowlie said the Go Get Funding page is a hoax.
"I'm so disappointed and angry that people can disrespect and exploit such a tragedy," she told The Herald.
A fake Facebook profile under Susan's name was also created, with links sent to the hoax fundraising page, she said.
"This has deeply hurt myself, my family and my late daughter's friends. Her babies do not deserve this."
The Go Get Funding page had an identical caption to the Givealittle page, underneath a picture of Kelsi and her surviving children.
Friends of Kelsi have warned others not to donate to the page.
"Sadly some small-minded, selfish people in the world have decided to take advantage of this tragic situation," a friend wrote online.
"The Givealittle page is the only page that is set up for Kelsi, and will remain the only page.
"Thank you to the people that have donated and to everyone who has taken the time to share it, we have been blown away by all of your support."
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Susan Fowlie earlier told the Herald Wood gave her life rescuing her daughter from the sea.
"Our dear Kelsi was a strong and fiercely independent woman with an intelligent mind and good values. A most incredible mother who loved unconditionally."
"I am so heartbroken. She leaves behind three beautiful children, family members, partner and friends ... we are lost for words."
Wood had been through a fair share of hardship, but always looked forward with a positive spirit, her mother told the Herald.
"She was amazing ... I will miss her for the rest of my days."
No money has yet been donated to the Go Get Funding page. Go Get Funding has been approached for comment.