You need to edit your theme.html file and remove the lines that call the image as follows: (taken from default theme. This may vary)
<table cellspacing="0">
<tr id="footerbar">
<td><a href="https://xoops.org/" target="_blank"><img src="<{$xoops_imageurl}>poweredby.gif" alt="" /></a></td>
</tr>
</table>
Now save the file and save back to the server. You will need to make sure that you have "update theme.html" set to 'yes' in your admin preferences. You may also need to delete the files in template_c and purge your browser cache befor you see any changes.