The simplest way would be to create a copy of the group widget from within your child-theme functions.php file.
By doing this you can hardcode whatever you need to the original html. Once done, you use your widget instead the original widget. Only thing you have to take care is the function name which should be unique.
And voilĂ .
Of course, if you are a php ninja, you can probably extend the BP_Groups_Widget
class to get the same result. Many examples here.