Branches can be removed from a TFS project by converting them back to a folder. This is usually done when a branch was created by accident and needs to be removed. The tricky part is when the Convert to Folder menu option doesn't appear. If you find yourself in this situation you're most likely using the context menu (right-clicking). Try navigating to File -> Source Control -> Branching and Merging. You should see Convert to Folder there.
I'm not sure if it's true but a colleague of mine told me that Microsoft purposely did this to help avoid accidental conversion of branches to folders by making it harder to get to the command. It also helps make it very confusing and frustrating - IMHO.