How do I edit the query for a Query Table after it has been created?
How do I permanently delete a Query Table? Even after I do right-click -> remove, it still appears in dropdown lists.
It is impossible to edit the query table after it was created in ArcMap. You might like using Query Layers available since ArcGIS 10.0 - there you can edit the SQL expression used by going to the Layer Properties window > Source tab > Change query.
Not exactly sure what drop-down list you refer to.