I am getting a threat from someone claiming that my website is infringing on their trademark. Should I just ignore them? I want to avoid court if possible.
Are you sure you aren't infringing on their trademark? Ask your lawyer, and if he agrees with you, get him to write a letter to the threatening party.<p>And really it depends on who is doing the threatening. It's your call as to whether they are serious or not; but if you have a lawyers opinion that you are not infringing, then they are much less likely to waste their time and yours in a legal action they would likely lose.
What kin of threat, email from the webmaster, letter from a lawyer? Specifics, including the URL, will better shape the answers here. In any case, advice from a lawyer trumps advice here.