Login to your admin cp and find your navbar template.
Find:
Code:
<if condition="$show['notifications']">
<div><span id="notifications"><a href="usercp.php$session[sessionurl_q]">$vbphrase[your_notifications]:</a> <strong>$notifications_total</strong></span></div>
Replace with:
Code:
<if condition="$show['notifications']">
<div><a href="usercp.php$session[sessionurl_q]">$vbphrase[your_notifications]:</a> <strong>$notifications_total</strong></div>
I tested it in 3.8.6 it should work and just give you a link.
It removes the graphic but the drop down does not work after that. Its the only way to get rid of it that I see though. So you will have to decide if the drop down is important to you.