The Tahr Foundation has apologised for any offence taken after adopting the lobby slogan 'They Are Us'.
The Department of Conservation plans to cull the introduced species at three times the level it has in past years to bring the population down to a more sustainable level and protect South Island flora and fauna.
However, the foundation wants people to regard tahr as a special part of the country, because they have lived in New Zealand for more than a century.
Its latest campaign video was given the same name as the country's Quote of 2019, coined by Prime Minister Jacinda Ardern to promote unity after the Christchurch mosque attacks.
The video was renamed 'What They Mean To Us' after six hours online with thousands of views and shares.
Spokesperson Willie Duley said the foundation was "completely unaware" the phrase was often used in reference to the mosque attacks.
"We did have a couple of people saying the 'we are us' term was linked quite close to the Christchurch tragedy and that some people might take offence to that. We clearly did not mean any offence, so we changed it immediately. The reason we used it was because, for many of us, tahr are part of the fabric of New Zealand. They're part of us. They are us," he said.
"We apologise wholeheartedly if there's any offence taken there."
Central to the video is the idea that tahr are "part of the fabric of society" since being introduced in 1904.
Conservationists said the same theory wasn't applied to rats, stoats, and other problematic pests, but Duley said "you've just got to be realistic."
"Are rats, stoats and other pests valued by people? Not really. Are tahr valued by people? Yes, by the thousand ... there's a $100 million hunting industry out there that draws a huge income from tahr."
Earlier this year, Forest and Bird sought a high court declaration claiming DOC's plan was illegal because it did not go far enough.
It declined to comment on the Tahr Foundation's video.