Employees for weight-loss company Jenny Craig have also been told their services will continue during the lockdown.
Wellington branch manager Linda said she didn't think the company was an essential service.
"I was shocked to be completely honest, because I had assumed it was in there, black and white, what the government had released.
"Food delivery is prohibited unless it's an essential service and we are a weight-loss company. It's not directly for food and convenience. We are not a delivery food company."
According to MBIE guidelines, food delivery is prohibited except for supermarket deliveries, Meals-on-Wheels and whole food delivery services.
Linda said the company had applied for wage subsidies, and employees could choose to stay home if they wished.
But she said she was concerned for the safety of the employees who chose to work and for their clients, because she didn't believe the company was putting them first.
"When we were on a level three alert, I sent an email out to my chief executive asking if we could do strictly phone calls for clients and phone delivery and I was denied that," she said.
"I was told that we could offer them that but that one on one support is crucial. During these conversations there was nothing for the safety of my team or myself other than that we were allowed a $10 to $15 float to go out to the supermarkets and try to find as many sanitising products as possible."
Linda said she loved her job, but felt strongly that its services should not be continuing during the lockdown.
"I don't mean anything malicious and I don't want to shame the company at all because I wouldn't work for the company if I didn't believe in them. It is an amazing brand to work for, but just not at this time. We are not essential and I've said it many times."
E tū union lead organiser, Mat Danaher, said it appeared Jenny Craig was stretching the envelope to be considered an essential service, and it was working with the company's employees for some clarity.
"I sent an email to Jenny Craig to get their side. They said they had applied for registration but their view was that they could keep operating until they got the registration back," he said.
"Well, that's wrong, it should be the other way around. They should stop until it is confirmed they are an essential service."
MBIE did not explicitly confirm whether Jenny Craig could remain open, but said delivery of prepared meals that are pre-cooked are the same as takeaways and are not covered.
In the meantime, 18 of the country's 21 Jenny Craig centres remain open.
Storage facility staff told they are an essential service
Some employees are refusing to work because they don't believe their jobs are an essential service.
Among them is 68-year-old Charlee Kelso, an employee at National Storage, who said she was shocked when the company informed her it would be business as usual during the lockdown.
"National Storage have not cared enough, making us all go to work, saying that we're essential and we're not," she said.
"The only thing that I can do is clean and open up units that are in arrears and to me it's not essential. It's essential for National Storage to get their money in but it's not essential as in, life or death.
"I don't want to get the virus, and I don't want to give it to anybody."
National Storage said in a statement it was an essential service, after the government announced self-storage facilities can operate to facilitate access to essential items.
"We have been in ongoing dialogue with the relevant NZ government ministers, to confirm the critical role which self-storage plays in the essential services storage, supply and logistics chain.
"We are acutely aware of the need to play our role as part of essential services distribution chain, as well as providing individual customers with access to their own essential items which they may currently have in storage."
The company said it had a range of safeguards in place for staff including online processing for customer inquiries and social distancing measures.
It also hasn't needed to make an application for wage subsidies.
But Kelso said the company hadn't considered staff who weren't critical for the operation of the business, and she had made the difficult decision to stay home without pay.
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"I've decided to go with my family first," she said.
"I've actually rung Work and Income today to see if I can get help with my rent especially. Four weeks is gonna really put me back, but it doesn't matter, it's the principle of the thing. The government has given our employer the opportunity to get money for all of us.
"As an employee they can help me, but they don't want to. We work hard for our employers. I really enjoy working for my employers. I'm really quite sad and I was in tears yesterday."
In a statement, MBIE confirmed self-storage facilities can operate only to facilitate access for essentials.
"Access to existing lockers is permitted for essential items and services only, for example retrieval of a fridge to replace a broken one. New sales or expiries of units are considered non-essential business.
"The business should look at alternate ways to manage these aspects such as renewing expired contracts remotely. While providing access to essential items for the public, it has to be done in a way that limits the transmission of Covid-19."