As Director of a domain name protection company (and not an attorney) I can offer this:
If you registered the domain name before the other party files for a trademark, then there is no way you would have known that they would file for the mark. So, in most cases you probably don’t have to give up the domain name. It comes down to whether or. Or you registered the domain “in bad faith” or not. And again, how would you know they would start their business and get a trademark? You wouldn’t.
Are you in the same industry and compete with each other? If so, there might be an issue, but I’d your site offers different products and there would be no confusion between companies or websites, then there may not be an issue.
The best way to handle this is to get a domain name attorney to respond to their letter to you, essentially telling them to go away, and that you plan on keeping the domain name.
If you cannot afford an attorney, look for a company that offers domain name insurance or a domain name warranty, if you have an issue like this with your domain name, your legal fees to defend the domain are covered.
As you have described the situation here, you bought the domain before they filed for their trademark, and you’re not pretending to be them. So you should be able to keep the domain. They are just trying to “ strong arm” the domain away from you with a threatening letter. If they do sue you or file a udrp, defend yourself with the help of a good domain name attorney.