Best way I've found to eliminate that is to go to settings in ADW and totally eliminate the trash can...you can still delete stuff with a long press. The trash can just gets in the way.I delete that app drawer button all the time, but it's just a widget, so I just reinstall the widget there, no need for a full-on restore.
UI setting>trash can position (all the way to the bottom) and select 'NONE'.