The letter signed by project manager Simon Kirkpatrick, said "some 13 full-time positions" may no longer be available.
The Times-Age was previously told the project employed 30 people, of whom 25 were from Wairarapa.
Mr ten Hove said any issues related to employment were between the staff and the company.
"I'm not in a position to comment on what the company tells its staff," he said.
However, he confirmed the contractual difficulties referred to in the letter were related to the Beca Carter Hollings and Ferner (Beca) saga.
The cost of the project was underestimated by the consultancy company by up to $6.6 million. The council is in legal proceedings with it.
Mr ten Hove said issues with the construction of the new ponds had been previously reported and included delays related to weather.
"There's nothing new here from the council perspective," he said.
Mr Kirkpatrick said he was unable to make any public comment. The Homebush site is a wastewater treatment plant, and the upgrade involves decommissioning ponds and building new ones. It is the single biggest project undertaken in the district's history.