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That's the way the "Add to Home Screen" option works, it adds an icon to your home screen so you can quickly access the website from there.
In your Site Settings App you can notice Mobile Touch Icon field, that's exactly the file used for a web page icon on the Apple iPhone, iPod Touch, and iPad when someone bookmarks your web page or adds your web page to their home screen.
Hope this cleared things out for you, Karim!Reply