Hi,
Thanks for purchasing our plugins. I can help out here.
All our main event views (month, list, etc) are setup as archives and not pages in WordPress.
The templates can all be moved from the plugin to a child theme to be edited without losing changes on updates.
We have the themer’s guide here to explain that process:
https://theeventscalendar.com/knowledgebase/themers-guide/
And we also have these conditionals to target different views so you can add content just for those pages:
https://gist.github.com/jo-snips/2415009
Let me know if you have any follow up questions.
Thanks