How do I change the visibility status of a published template?

Click on "Tools" and the click "Template Library" in the left menu. Then go to "Published templates" and unpublish the template by clicking "Unpublish" on the right of the template name.

Then go to "Publish template" and select the template you want to publish by clicking "Publish" on the right of the template name.

Select privacy level and click "Publish".