Can You Offer a Little Help With Site Category Dropdown CSS?

I am attaching a screenshot. I would like #1 to look more like #2 - transparent background instead of surrounded by white. The white is caused by the widget class - but as it controls the appearance of all the widgets in the sidebars, I would prefer not altering it.

Could you offer any suggestions on how to rid your widget of the white background surrounding it?

Thanks
Arizona