I don’t know if your theme has provision to specify the custom css or not but you can certainly edit the theme stylesheet and do this.
Hope this helps!
Try doing following
// specify id if you are using outside post loop
// otherwise keep it as get_permalink()
$permalink = get_permalink( $id );
// printing output
echo str_replace( get_bloginfo( 'url' ) . '/' , '', $permalink );
See if this helps!
What you can do is simply use anchor tag <a> within your <div> which holds the background image and apply the same css that you used for the div to anchor tag and comment the css on div.
See if this helps.
[Please post markup snippets between backticks or use the code button.]
