Find and remove in your "FORUMHOME" template:
<if condition="!$show['guest']">
<table cellpadding="0" cellspacing="0" align="right" width="100%">
<tr>
<!-- member logout -->
<td align="$stylevar[right]">
<a href="login.php?$session[sessionurl]do=logout&logouthash=$bbuserinfo[logouthash]" onclick="return log_out()"><phrase 1="$bbuserinfo[username]">$vbphrase[log_out_x]</phrase></a></td>
<!-- end member logout -->
</tr>
</table>
</if>