On my iPhone I normally close all open apps I am not using by going to the open apps screen and swiping up. What should I do about the TRUCE App?

You should not swipe up on the TRUCE App as it will show as an attempt to kill the app and be reported to your supervisor. TRUCE will restart automatically anyway. It may take a little getting used to, but it will typically end up all the way on the right of the open apps and you can ignore it. As mentioned previously in the Battery Consumption section, TRUCE uses very little battery when you are not in a managed session.