First let’s start with “what is a troll?” http://en.wikipedia.org/wiki/Troll_(Internet)
The number on rule is “don’t feed the trolls.” This doesn’t mean never respond but responses must be well thought out and diffusing. Nicer instead of simply defensive (but do not admit wrongdoing if there was no wrongdoing.)
Since some trolls will persist if you simply don’t respond, your next best bet is to move the conversation out of the public view when possible. But be aware that your private messages may get reposted publicly if a troll is particularly nasty.
Boilerplate for trying to get a troll into a private discussion:
“Can you email this and any additional information you have to our ___ department so it can be properly reviewed? Here’s the email address ________”
As for whether or not to delete a troll’s comments, the general rule of thumb is to leave it be. There are instances where deleting something (or more likely deleting something after a period of time) is ok but that decision has to be made on a per case basis.
Yes, they might have made false accusations that may make you look bad but your response can still be civil and indicate that you may be dealing with a potential crazy or that you are willing to deal with the situation if something IS actually wrong.
Example false complaint:
“You took a photo from my website. That’s not legal.”
Example response to a false complaint:
“To the best of my knowledge all our photos come from the manufacturers, photos we’ve taken or stock photos aquired through proper channels. We take copyright ownership seriously. Can you email additional information and links to the photo in question to _________? We would be happy to review this.”
(Side note: You do know that you can’t take a photo from any random website and use it right? Just checking to make sure you do know that. Your staff should know that as well.)
When in doubt, don’t respond immediately or delete. Getting defensive or deleting the post will likely only make things worse.