Disable views stripping style=""

I'm setting up a customized view and want to use style="" for one part (see code below):
<div style="background: url(/[field_featured_image_fid]) no-repeat top left #9ac03c;" id="featured-background"><div id="featured_left_panel"><div id="related terms">[tid]</div><div id="featured_left">[field_featured_left_value]</div><div id="view-study">view case study</div></div><div id="featured_right_panel"><div id="title">[title]</div><div id="featured_right">[field_featured_right_value]</div></div></div>

I could use views template for this and have it work; however, "rewrite the output of this field" does 99% of what I need. Everything is displayed properly with the above code except the first tag which become <div id="featured-background">. Does anyone know how to disable the removal of style tags and why this useful function is disabled?