Quote Originally Posted by HeathenMagic View Post
tpl_appletouchiconpng_default.php
When Apple-products try to surf around your site, instead of looking for favicon.ico files first, they look for apple-touch-icon.png files.
If you create that file, then this specific issue will go away.

Actually they look for lots of variants of that file, including the following (and probably more):
apple-touch-icon-180x180.png
apple-touch-icon-152x152.png
apple-touch-icon-120x120.png
apple-touch-icon-76x76.png
apple-touch-icon-57x57.png
apple-touch-icon.png
touch-icon-192x192.png


And microsoft devices (windows phones, surface tablets) look for:
ms-tile-image144x144.png

And they all look for favicon.ico too.

So the solution is simple: use an icon-capable graphics program to create appropriate variants of your store logo for the corresponding dimensions and filenames, and put them on your server.
There are hundreds of online articles on how to do this, including dozens of software programs that can do it. Some free. Some with crappy adware. Always use caution when installing new software.