To eliminate the popup, you could probably just comment out lines 77-78 of the plugin's PHP file, which should be in this directory:
www.yoursite.com/components/com_comprofiler/plugin/user/plug_cbconnections
The lines are:
[code:1]$tooltip = cbFieldTip($ui, $tipField, $tipTitle, $width='250', $icon='', $htmltext, $href, $style='', $olparams='',false);
$return .= $tooltip;[/code:1]
If you wanted to tweak the default style instead, it looks like you'd have to edit overlib_mini.js file in the js folder of the component.