You would need to do this manually by implementing a custom creation filter and assigning an instance of it to the CreationFilter property of the toolbars manager. Here is a filter that should remove the button:

public class MyCreationFilter : IUIElementCreationFilter
{
 void IUIElementCreationFilter.AfterCreateChildElements( UIElement parent )
 {
  if ( parent is RibbonCaptionAreaUIElement )
  {
   for ( int i = 0; i < parent.ChildElements.Count; i++ )
   {
    if ( parent.ChildElements[ i ] is QatQuickCustomizeToolUIElement )
    {
     parent.ChildElements.RemoveAt( i );
     break;
    }
   }
  }
 }

 bool IUIElementCreationFilter.BeforeCreateChildElements( UIElement parent )
 {
  return false;
 }
}