This new service is a minefield. One you would be wise to stay away from.
According to the website, the ultimate goal is to, “encourage useful discussion that resolves difficult workplace issues. We provide a safe environment in which to do that.”
However, safe doesn’t necessarily mean completely anonymous. The site claims, “Unless required to by law, we will not reveal your identity.”
The service, as noted in this LifeHacker.com article, might reveal the sender. “The catch? Tell Your Boss Anything flags messages with violent phrases or cursing, and if a manager flags a message because it’s abusive, Tell Your Boss Anything might reveal your identity. Keep a level-head if you decide to fire off an email to your boss.”
If you’re going to be level-headed, why not have a conversation with your boss instead? Not to mention, if you’re in a small department or have a unique writing style you’ll be giving yourself away.