The control in the upper right corner is called “NavigationControlPanel”. It consists of many NavigationControls.
NavigationControlPane.getNavigationControl(NavigationControlType.TIME_SPAN).setVisible(false);
Ideally you create your own instance of IComponentFactory (subclass DefaultComponentFactory) and override the createLayerContainerCorner() method. Inside this method always call super.createLayerContainerCorner(). When the corner is “UPPER_RIGHT” you can cast the returned component to NavigationControlPane and call the above method.