When control is a ToolTip, the bounding box background is white and has a border. We can define a style to remove.
<style x:key= "Tooltiptransparentstyle" targettype= "ToolTip" >
<setter property= "Background" value= "#FFF7F8FA"/>
<setter property= "Padding" value= "0,0,0,0"/>
<setter property= "borderthickness" value= "0"/>
<setter property= "BorderBrush" >
<Setter.Value>
<lineargradientbrush endpoint= "0.5,1" startpoint= "0.5,0" >
<gradientstop color= "#FFA3AEB9" offset= "0"/>
<gradientstop color= "#FF8399A9" offset= "0.375"/>
<gradientstop color= "#FF718597" offset= "0.375"/>
<gradientstop color= "#FF617584" offset= "1"/>
</LinearGradientBrush>
</Setter.Value>
</Setter>
<setter property= "Template" >
<Setter.Value>
<controltemplate targettype= "ToolTip" >
<border x:name= "Root" borderbrush= "{TemplateBinding BorderBrush}" borderthickness= "{TemplateBinding BorderThickness} "cornerradius=" 2 ">
<border borderthickness= "1" cornerradius= "1" padding= "{TemplateBinding Padding}" >
<Border.Resources>
<storyboard x:key= "Visible State"/>
<storyboard x:key= "Normal State"/>
</Border.Resources>
<contentpresenter cursor= "{TemplateBinding Cursor}" contenttemplate= "{TemplateBinding contenttemplate}" content= "{TemplateBinding Content}" margin= "{TemplateBinding Padding}"/>
</Border>
</Border>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
When creating a ToolTip instance, use this style on the Tooltip.style.
Reference: http://www.cnblogs.com/eagle1986/archive/2012/05/12/2497189.html
Siverlight remove the white border of the ToolTip