You should worry, but for different reasons. I strongly recommend uninstalling Avast immediately.
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Doubtful it's a virus.
Make sure your Mac's software is up to date.
Open the App Store then select Updates from the menu.
Also, if you are using Safari to surf the net, you could have a Safari extension or third party plug-in installed that's causing this glitch.
You are using the Avast antivirus software. It adds a "man-in-the-middle" security certificate, intercepting all of your traffic. You can read more about that here: http://www.thesafemac.com/avasts-man-in-the-middle/
Question: The green lock next to Apple website isn’t there