Ministry emails revealed by 1News showed a top advisor criticised the quality of information Costello provided to justify cutting tax on the heated tobacco products.
Earlier today, Health Minister Shane Reti joined Costello and Prime Minister Christopher Luxon in questioning the professionalism of ministry staff.
Labour leader Chris Hipkins then questioned Luxon in Parliament over who provided the heated tobacco products advice, and whether any conflicts of interest were being appropriately managed.
"If he doesn't know who's providing advice to the minister, how can he be confident that conflicts of interest are being appropriately managed?" Hipkins asked.
Luxon replied: "Because I know that that minister is determined to lower smoking rates across this country and is doing so incredibly passionately and is determined to do it. I'd just say to that member, if he cares a lot about conflicts, I wouldn't call a sister-in-law a 'distant relative'."
The comment referred to Hipkins' initial characterisation of Labour health spokesperson Ayesha Verrall's sister-in-law - who was one of the Ministry of Health officials advising Costello on tobacco reform - the day the matter was first raised.
Hipkins said family should not be brought into the debate.
While Luxon protested that he did not name anybody, the Speaker asked him to consider the inference.
Luxon withdrew his comment, and apologised to the House.
Meanwhile, public servants today complained of "a chilling effect" on democracy after Costello accused health officials of "yet again" undermining her efforts to reduce smoking rates.
Public Service Association national secretary Kerry Davies said Costello's remarks were outrageous and "unacceptable within our democratic system".
Addressing reporters at Parliament this afternoon, Costello described some of the ministry's work on smoking reform as "unhelpful".
"It was just revisiting stuff that didn't need to be revisited," she said.