if you can access this private person, then go into edit mode, and over on the right, you should find his name and the option to add/remove. IF you choose to remove this will only unlink the person from your tree, but will not delete the profile altogether.
If you cannot access this person because he is private then you need to contact the other Profile manager, and either ask them to unlink their private person from your tree, or to explain why he was added and provide sources. and from there you an ask to be out on the trusted list and when that happens, then you can unlink him yourself. But make sure that you explain to the other PM what you are doing and why.