You need to take out the dollar sign.
<%if isLinkOwner%>
<%body_font%>
<small><a href="<%db_cgi_url%>/modify.cgi?LinkID=<%ID%>">
Edit this link</a></small>
<%endif%>
<%if isLinkOwner%>
<%body_font%>
<small><a href="<%db_cgi_url%>/modify.cgi?LinkID=<%ID%>">
Edit this link</a></small>
<%endif%>