Here is the reply provided in the support ticket:
By design there is no way to edit a page template using Editing tools. If you edit a content block placed in a template the changes will affect all the pages which using this template. Because of this the only available option to edit a template is to do it in the backend. The actual problem is that the Edit button should not appear when the content block is on the template.
Keep in mind that this discussion is related with our old implementation of inline editing.
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