@Macmanx, OP states "...it showed ONLY image, and that's how I want it". Wouldn't un-checking "Show Link Image" produce the opposite of the effect he's looking for?
I'm having the same issue - I think. I just started using the links widget, so I don't know what it looked like before. I ONLY have "show link image" ticked (everything else is clear) but the "link name" displays anyway. If I remove the link name info, the widget displays the URL.
I am curious - when this widget worked properly, how did it lay out the icons? Were they stacked vertically or did they form a 'grid'?
I would like mine to display flush up against each other on all sides, like a 'mosaic', but I'm having a hard time finding the code that determines how it displays.