I am only versed in ADT 3.3 on 2002, so what I say might not hold true for 2004 ... anyway, in the style settings you should be able to manipulate the visibility of certain aspects of the AEC object by opening up the Slab Styles ... I believe it is AECSLABSTYLE
In the resulting windows, double click on the slab style you are using, select the display property tab, then select either the system settings or the custom overrides and turn off the component you don't want to be visible.
If you can post a file or screenshot showing exactly what you are talking about we might be able to offer more guidance.
Oh .. and welcome to the swamp