It appears your theme's social media icons in the upper right corner are using very non-specific CSS that is thusly also applying to the elements within this widget.
You have this on line 756 of style.css:
Since that applies to every single element with the class "twitter", it's also applying to your brankic social media twitter element.
Hopefully you can change the CSS for those icons in the header to look like this instead:
I'm guessing you'll need to do the same for the Facebook icon:
That change will make the background-image only apply to .twitter and .facebook elements found within the div with id='social-media-icons'