I found this: http://www.intelproplaw.com/ip_forum/index.php?topic=11975.0

"...if you received your trademark registration after the domain name was registered, you will not have a solid case for a domain name dispute unless your mark was famous or well-known prior to the date the domain name was registered"

Still there seems to be special cases where the guy having the domain is deliberatively taking advantage of your business name. Those are considered case by case by an attorney without clear-cut rules. Consequently, in your case, if you're clearly taking advantage of their name on purpose, trying to confound people etc, they could sue you and get the domain.

Trademarks are not used for extortion. A registered trademark is use to protect a corporation, company or other entity's brand & reputation. Otherwise, everybody and their momma would be free to use it. If you feel that someday your brand or company as potentional to suddenly take off &/or become popular, either as franchise or brand recognition, it's advisable that you go ahead & register your trademark with USPTO from day of founding the company and/or brand. The corporation,company or individual business entity has to protect their positioning & brand reputation from others who otherwise might have different motives to take some of that corporation's mineshare or damage their reputation.

It seems I can't vote for the question, but I'm looking for the same. The question is clear and hasn't been answered yet. Does registering a trademark after someone else has registered a domain, have some legal rights over the domain? (so it is not how trademarks are used but if they can be used to claim an already owned domain).