Click Tools > Template Library in the left-hand menu. Click on the "Published templates" tab and then the "Unpublish" button to unpublish the template for which you want to change the visibility status.
Note that when you choose to unpublish templates, they remain in the organisation and with organisations that previously chose to save them.
Then, click Publish template and "Publish" on the template you unpublished.
Enter a title and a description, select visibility, and change it. Continue by clicking the "Publish" button.