Besides closing the Popup Window via buttons that manipulate the IsPopupOpen property of the RadPickerBox control,
you can allow the user to close the popup by clicking on the Back button of the phone. By default this action is allowed. If you want to disable it, set the
IsPopupClosedOnBackButton to False.
Here is an example.
<telerikPrimitives:RadPickerBox x:Name="radPickerBox" IsPopupClosedOnBackButton="False" />