Bettina Arndt’s Order of Australia has been referred to the independent body that hands out the awards amid growing calls for the controversial sex therapist and writer to be stripped of the honour.

Arndt was criticised last week after she congratulated a Queensland detective who said police would keep an “open mind” in a case where a man allegedly killed his wife and three children by dousing them with petrol and setting them alight.

On Monday the office of the governor general, David Hurley, confirmed he had referred correspondence over Arndt’s award to the Council of the Order of Australia.

“In all matters relating to the Order of Australia, the governor general acts on advice from and recommendations made by the Council for the Order of Australia,” his spokesman said.

“When the governor general receives correspondence – including requests to terminate or cancel an award – it is referred to the council … for advice and action.

“Following this standard process, the governor general has referred correspondence in relation to the appointment of Ms Arndt to the council.”

The Victorian attorney general, Jill Hennessy, had already written to Hurley asking him to rescind Arndt’s honour over a controversial interview she conducted with twice-convicted paedophile Nicolaas Bester in 2017.

A senior Queensland police officer is stood aside for doing his job professionally and telling the truth about how an incident should be investigated. This could well be a tipping point. I constantly hear from police appalled at being required to impose unjust laws and... — Bettina Arndt (@thebettinaarndt) February 21, 2020

But Ardnt’s comments congratulating a policeman for heavily criticised comments suggesting police were keeping an “open mind” over whether the death of Hannah Clarke and her children was a case of a “husband being driven too far” has prompted further scrutiny over her award.

“Congratulations to the Queensland police for keeping an open mind and awaiting proper evidence, including the possibility that Rowan Baxter might have been ‘driven too far’,” Arndt said in a tweet.

“But note the misplaced outrage. How dare police deviate from the feminist script of seeking excuses and explanations when women stab their partners to death, or drive their children into dams, but immediately judging a man in these circumstances as simply representing the evil violence that is in all men.”

Ardnt’s comments prompted the Victorian state Liberal MP Tim Smith to also write to Hurley asking him to formally rescind her honour, and the federal Liberal senator Sarah Henderson also said she should be stripped of the award.

Upon further reflection I think these comments are so grotesque that this woman must not be awarded an AM, which was announced on Australia Day. I hate saying that, but she must not be recognised in any way as an outstanding Australian. https://t.co/tub8RixMzL — Tim Smith MP (@TimSmithMP) February 21, 2020

Today I wrote to the Chair of the Council for the Order of Australia to formally ask the Council to advise the Governor-General that Bettina Arndt’s AM be cancelled because of her comments that sought to excuse extreme violence. Her comments will “bring disrepute on the Order.” pic.twitter.com/fizGF1fP7o — Tim Smith MP (@TimSmithMP) February 22, 2020

My letter to the Chairman of the Council of the Order of Australia Shane Stone. Ms Bettina Arndt’s award as a Member of the Order of Australia in the General Division should be cancelled. pic.twitter.com/8vlUdJFtdy — Senator Sarah Henderson (@SenSHenderson) February 24, 2020

The policeman praised by Arndt, Det Insp Mark Thompson, was stood aside by Queensland police after his choice of words sparked outrage.

Katrina Carroll, the Queensland police commissioner, said he had volunteered to step down “for the integrity and the confidence” of the investigation and of Queensland policing more generally.

She said Thompson was “an extraordinarily committed, experienced and brilliant investigator” and “an exceptionally good police officer” who was distressed and distraught by the consequences of what he had said.

Arndt said: “We need to stand up to this dangerous mob rule and demand Mark Thompson is reinstated.”

Clarke, 31, and her children, Aaliyah, 6, Laianah, 4, and Trey, 3, died after Baxter allegedly poured petrol on his family and set them alight at Camp Hill in Brisbane last week.

Baxter died on the footpath from self-inflicted wounds, police said.

Arndt has been contacted for comment.