Roofing Company Wants To Charge 3x After Job Completed Without My Approval

I'm speaking on behalf of my sister. She had her roof replaced by this company called HomeFix out of Maryland. Her roof needed some repair and they quoted her for $9k. She signed a contract that stipulated any additional cost for unforeseen damage will increase the quote (obviously), but that they would first have to get owner (my sister's) approval. This is in Virginia btw.

They began construction and when they removed part of the roof then found rot on the wood and told my sister they would need to remove all of it and that they would increase the estimate. She replied for them to not continue doing any more work. They didn't listen and continued to rip out the roof until the home was exposed. Snow was set to fall that night and so they told her they had to finish it because they couldn't leave it exposed. But she said she had already told them not to continue from the initial discovery over rot, whereby they could've put a tarp.

Anyway, they continued working on it without my sister's permission and now are charging her $27k. And that down from the $34k they wanted to charge her (after much discussion on her part). Is there a way for her to win legally or are these big construction companies able to weasel their way out of this? The contract states any additional work that’s done needs to be approved by the owner first, and my sister didn’t give them any form of approval before they continued working on the roof.