Representatives of the council arrived on their door step last week to discuss the eradication of their nests.
Ms Burgess was told she would be fined or arrested if they attempted to interfere under the Biosecurity Act 1993.
"I do not want a helicopter flying low and poisoning the wonderful birds, I feel like we're under attack," she said.
Rooks are a designated pest under the Hawke's Bay Regional Pest Management Strategy, which means whether they are a problem or not they have to be controlled.
Animal pest advisor, Dean Roughton, said it was their responsibility to eradicate rooks across the region and have a programme in place, which aligned with the other regional councils.
The birds were deemed by the council as highly damaging both economically and environmentally, as they ruined the crops on farms by flicking the seedlings out.
Ms Burgess wanted to know why they could not just go to the farms that saw them as a pest.
Mr Roughton said it would be impossible to only eradicate nests on certain farms, as they were a very good breeder and could fly long distances. "If we left the birds uncontrolled we would have five times the amount we had the previous year, which we cannot have."
The Maraekakaho farm had been in the family for 150 years and Mr Paterson said the rooks were a part of his childhood.
"I remember listening to them as a child, it was a very comforting sound," Mr Paterson said.
The council are taking submissions for their pest management strategy next year in June, when the couple are hoping to take a formal stand.
"If anyone else feels the same we encourage you to join us in getting our opinions heard."