Hi @JasonMayes. That is a property of the Parameter API object called ExposedAsProperty, which has a Read/Write Boolean type value. There are lots of examples of how to access and change that property here on this forum.
Dim oParams As Inventor.Parameters = ThisDoc.Document.ComponentDefinition.Parameters
Dim oParam As Inventor.Parameter = oParams.Item(1)
'this next line will 'toggle' that setting every time you run it
oParam.ExposedAsProperty = Not oParam.ExposedAsProperty
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Wesley Crihfield

(Not an Autodesk Employee)