To remove a field from the setup, first select the feature class,and then find the field in the field mappings grid. Then, you will delete all of the text from both the "Feature Class Field Name" column and the "Linked Code/Type Field Name" column. Do not leave any spaces in this field; you will need to clear the field out completely.
This does not delete the field from the feature class. You are still responsible for deleting the field from the feature class (if needed) in ArcCatalog.