If you edit the template which contains the fields you want to remove you will see two buttons just to the left of the Push Left/Right buttons (<>). They look like a pencil with an eraser at the end. These allow you to reset a single field or all fields in a template.
To reset a single field click on it in the sample line and then click on the button with the single line being erased.
To clear all fields click on the button with multiple lines being erased.
Bill is right except that in V6 you won't see the 'move field' buttons afaik.
However the reset button does exist or you can delete the field using the Field List feature. Or simply go into the Template definition screen, place the cursor somewhere in the masked area of the field you want to delete and hit the delete key. You may need to tidy up in other places if the field is referenced by a formula, sort, filter, etc.
The inbuilt Help file covers some other options under the 'Move a Field Definition' subject under 'Creating Data Extraction Template'in Chapter 1. That section also explains how to redefine a field by deleting and recreating but retaining the same name. Personally I would move a field using the Field List if I remember the V6 Field List functionality correctly.
Later versions offer more possibilities to arrive at the same result depending on which screen you are using.