Mr Foss said he had been "very surprised" when Ms Lorck stood for the Labour Party because she had been "very supportive of everything we [the National Party] were doing".
Asked about the context of the tweet, Ms Lorck said it was posted after her daughter sang in the Frimley School Choir as part of a factory opening attended by Mr Key.
She did not delete the tweet when she announced she would stand for the Labour nomination.
"Speaking as a mum, it's really sad that Craig Foss wants this photograph to take away the pride a child has with standing with the Prime Minister of the day.
"Just because he's [John Key] got celebrity status doesn't mean I agree with how he runs the country."
Asked if she was ever a National supporter, Ms Lorck said: "I've never been a member of the National Party." However, the former PR consultant said she spent an hour on the phones encouraging people to vote on election day in 2011 after a member of Mr Foss' campaign team asked her to.
She said that was not as a National Party supporter because party campaigning was not allowed on election day.
"The Labour Party knows what I did and doesn't have a problem with it."
Ms Lorck said she decided to "stand up against the Government" at Frimley School two-and-a half years ago, after a rousing speech by the school's principal, Malcolm Dixon.
Mr Foss said he recalled Ms Lorck volunteering on election day in 2011.
"Every election we have lots of people helping us, of which she would have been one.
"That's why it's always surprised me that she put her hand up for Labour, knowing she'd helped us in the past."
Ms Lorck denied she had ever supported Mr Foss.
"I have not been a supporter of Craig Foss.
"In fact, I have been disappointed with Craig Foss' performance in the past three years.
"One of the main reasons I'm standing for Tukituki is because Craig Foss has not delivered."
Ms Lorck drew criticism from the National Party, including Mr Key, earlier this year for another tweet, also posted in 2011, which called David Cunliffe, now her party's leader, a "bully".
The tweet referred to the fallout of Mr Cunliffe's February 2008 decision, when as Minister of Health he sacked the board of the Hawke's Bay District Health Board. Mr Key said in April the tweet was an interesting reflection on the leadership of the Labour Party.