This Condition located on the Ministry category tab in Search Builder allows you find people who have any type of Contact 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 Contact. You would combine the Has Contacts 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.