I've been on the other end of this scenario. It was a couple of years ago, but I can't imagine much has changed. We held the trademark on the domain name—let's say we were ExtraSpecialVeeblefetzers.com, so a competitor opened up ExtraSpecialVeeblefetzers.co.uk.
So I dashed off a letter that we were going to file a complaint, not with the trademark office, but with ICANN. The reason this was a good way to go is that to even defend yourself in this kind of situation required a prohibitive amount of paperwork. I pointed out that whether we won or lost, he was about to be in for a huge, several-months-long bureaucratic pain in the tuchus either way.
The next day we got an email from him saying he'd reconsidered his strategy and "didn't feel good about" what he'd done, and he closed down ExtraSpecialVeeblefetzers.co.uk.
Your guys may not be as astute as I was. But they also don't have to warn you before filing the complaint. Personally, I would steer clear of it entirely, myself. For the few days he had it up, some of our customers began sending him really nasty letters (we had a lot of customer loyalty, it was a very well-liked brand.) People see that and they assume you're a creep... You might wind up losing more business than you gain from a stunt like that. People are savvy and don't trust doing business with people that can't succeed on their own merits.