"I believe they should have the right to organize," Clark said.
"We need to recognize that building trades are an important part of building the province. It's something that should be fixed and I'm going to get it fixed."
The B.C. and Yukon Territory Building and Construction Trades Council filed a lawsuit against the Crown corporation on Monday.
The suit claims conditions BC Hydro is imposing on companies bidding for work on the $8.8 billion project would prevent unions from organizing non-union workers on the site.
It also says they would bar unions not already present on the project from accessing the job site or worker accommodations.
The council is asking the court to declare that those terms violate workers' Charter rights to organize.
On Tuesday morning at the Legislature, Clark said she called BC Hydro CEO Jessica McDonald and that McDonald agreed to withdraw those parts of the proposal.
Major BC Hydro projects have historically been built under agreements with unions to prevent strikes or lockouts without banning organizing on site.