Deleting a template is the same process as deleting a project. You can open the template, open project settings, and then click "delete."
If you want to keep the template project, but remove access for others, open project settings:
Click "Use as Template"
And un-tick the checkboxes next to any groups you want to remove.
You should also un-share the template project to completely remove access.
If you delete a template project or remove access, it will no longer show up in template selection at project start.