"Cord blood is a valuable source of stem cells, which are a perfect DNA match for your baby," she says.
"By saving these stem cells it gives them the chance to survive many illnesses and conditions - now and into adulthood. You literally have one chance to do this and it's at birth so we absolutely want to take this opportunity. The collection kit arrived and it's definitely making me so excited for the arrival of our baby boy.
"Is cord blood banking something you have ever looked into? Would love to hear your thoughts."
The Hits host Laura McGoldrick and ZM host Megan Papas are among other high-profile mums to have also posted about the company, but complaints have only been made about Anderson.
The ASA said there were five complaints in total.
Chief executive Hilary Souter said the complaints were being processed with the chair of the complaints board still to rule whether the advertisement contained anything that could be a breach of the ASA's codes.
"Once this assessment has been made, the complainants, the advertiser, and the influencer will be advised either: that there are no grounds for the complaints to proceed or the complaints have been accepted for adjudication and inviting the advertiser and influencer to respond to the issues raised in the complaints. All relevant information is put before the complaints board and a decision made."
Casey McPike, of Outspoken, which represents Anderson for social media content creation and influencer marketing, said Anderson had met with CordBank owner Jenni Raynish to learn about the service "and the worldwide use of cord blood in treatments and trials for an increasing number of diseases and conditions".
She said Anderson, in her third trimester, and Forsyth had been aware of the benefits and were planning to do it for their son.
"They wanted him to have his cord blood collected and stored at birth so he would have access to his own stem cells for medical use in the future. When the opportunity came along to help CordBank raise awareness of cord blood banking, they were super keen to do that."
She said since posting on social media Anderson had had positive stories from other parents who have banked their cord blood, people wishing they'd known about it when they had their babies, and queries and views around delayed clamping.
Tauranga midwife Carmen Lett has been outspoken on social media about the company's choice to use influencers to sell the product, saying the benefits of it don't outweigh delayed cord clamping.
"It's guilt tripping mums into making them feel terrible about a choice that they can't even make because most people can't afford it," she has told her 10,000 followers.
McPike said: "We are aware of the social media content created by Carmen Lett – Carmen is of course entitled to share her opinions with her followers along with her own sponsored content pieces. As with TV, magazines, radio, billboards, websites – social media is another channel to communicate and one of the only ones that allows direct and immediate two-way feedback.
"Simone and Trent are happy with their decision."
She would not say what Anderson was paid for the post, citing commercial sensitivity.
McPike said she was unable to comment on the ASA complaints without knowing the specifics.
McGoldrick said she had been involved with CordBank since 2017, when she learned of the service through a friend.
"I spoke to parents who had used the service, about their experiences and reasons for choosing to use it. One of the things my research efforts showed, was that relatively few people knew they could access this service here in New Zealand, so I have worked with CordBank to help create some awareness of their offering.
"As with everything to do with child birth, expectant parents should do their own research, and find out if it's right for them."
Papas declined to comment.
Jenni Raynish, owner of CordBank said: "We won't be commenting on any of the complaints while they are still before the ASA."