I have made and used child theme of one WordPress theme. Later the parent theme got a new version and my client updated that which destroyed child theme’s customization. So I googled to Hide WordPress Theme Update Available Notification.
I got solutions regarding WordPress core and plugins update including action and hooks but didn’t get any simple trick to Hide WordPress Theme Update Available Notification. Later I realised that I could just edit the parent theme’s style.css and set the Version: to something ridiculously high from the WordPress specific CSS header right at the top. And the notification (and oh so dangerous link) went away!
So let’s say if your parent theme has version 2.2.5 at present and if you change it to Version: 9.9.9 (anything much higher than current version in ‘theme/style.css‘) then theme update available notification will be disable until theme author doesn’t release version 9.9.10.
I had a similar problem, but it’s more to do with the general annoyance of WordPress adding a new Twenty-x theme every year. It just adds bloat to the many sites I’ve built and maintain. I found you can quite easily turn the updates off by returning a null array to a filter ‘site_transient_update_themes’. This is the array list of themes that need updating. Setting it null makes WP think it’s empty. As this is a core filter you need to run it from a plugin.
I wrote a short blog post with the details here if you’re interested. http://morganleek.me/plugins/hide-wordpress-theme-update-notifications
Thanks for the information.