Take Down Notice of Website Due to Trademarked Name

I have gotten a domain with my personal money while I was working out a deal with a company. Before any contracts were signed, I paid for the website and started to design it. The deal didn't work out, so I had a domain which I had no purpose of. So since I paid money for it, I decided I would upload a picture of miley cyrus twerking for jokes.

The company wants me to take down the website due to copyrighted name. Nothing on the website itself has anything to do with the company.

What can they potentially do?

If you're squatting on their trademark, they can sue you.

As you're in Canada, go talk to a Canadian IP lawyer. You've already been reminded that this is a U.S. forum.