While that would work if you also unpublished the Breadcrumbs module do you also want the box with just the “Top” link in it?
If you want rid of the whole box please go to the Joomla admin panel and go to the template manager. Select the Ja anion template and click on the layouts tab.
Edit the default layout and remove the line in red as shown below.
<?xml version="1.0" encoding="utf-8"?>
<layout>
<name>Default</name>
<description>Default layout for JA Anion template</description>
<blocks name="top" style="xhtml">
<block name="header" type="header"></block>
<block name="cpanel" type="usertools/cpanel"></block>
<block name="mainnav" type="mainnav" markup="3"></block>
</blocks>
<blocks name="middle" colwidth="20" markup="3" fixheight="1">
<block name="content-mass-top" style="raw">content-mass-top</block>
<block name="content-top">content-top</block>
<block name="inset1" width="20">left</block>
<block name="right1" width="30">right</block>
</blocks>
<blocks name="bottom" style="xhtml">
<block name="botsl" type="spotlight" markup="3">user5,user6,user7,user8</block>
<block name="navhelper" type="navhelper" markup="3"></block>
<block name="footer" type="footer" main-inner="1"></block>
</blocks>
</layout>
Save that and you will no longer have that block.