This Condition, located on the Tasks and Notes category tab in Search Builder, allows you find people who have a Note on their record. The Comparison Values are either True or False.
You want to find everyone who has visited in the past month, but has not received a ministry outreach. You would combine the Has Notes Condition (setting the value to false) with a Recent Attendance Condition, perhaps for a specific Program and/or Division.
Search Builder has several other Conditions relating to Contacts. So be sure to look at all the options on the Ministry tab.
Updated for Tasks & Notes