You can edit the filter to blank it out and/or rename it but you can't actually delete it (I'll add a request to the Issue Tracker for that).
You can reset the search filters by clicking on the Reset to Default Configuration button in the Configuration window but that will reset all settings. To reset just the search filters you can edit the config.xml
file and delete the node:
<section name="PersistentFilters">
...
</section>
You might want to take a copy of the config.xml
file just in case things go wrong.