I’ve been customising a theme that had a new version, getting the message “There is a new version of … available”. I didn’t want the end-user to update the theme, because I’d customised it so heavily. I know that any updates are going to need to be done by a WordPress theme developer.
After a while of searching through code, looking for add_action and add_filter hooks, and even delving into the database, I realised I could just edit the theme’s style.css and remove the “Version:” line from the WordPress specific CSS header right at the top. And the notification (and oh so dangerous link) went away!
Summary: Delete ‘Version’ line altogether from the theme’s /style.css file.