If you create a diagram during your Free Trial or while on a paid account, your diagrams are by default Private.
You can quickly verify the status public/private status of a diagram by looking at the lock icon located next to the diagram name. If it shows a yellow, closed lock, the diagram is "private" and not publicly accessible on the internet. If the diagram has an open lock, it is public.
If your diagram is marked Public and you wish to make it Private, you can remove access to it at any time by clicking on Share.
Click on Deactivate Link. Click Deactivate Link again to confirm (you must deactivate each link individually currently). You can always regenerate a new code. This removes any public accessibility from the diagram.