Is it correct that they will sue you if you don't comply? Maybe, that's up to them.
Is it correct that your use of the domain name violates their trademark? Also, maybe. That depends on the market you are in, the market they are in and that the trademark is registered for, and other things.
If you aren't willing to just hand over the domain, and don't want to just roll the dice on liability, you should seek professional legal advice, and not respond in any way until you have received and considered that advice.