I think the bonus gained from a trophy should be the same as the bonus awarded from defeating a villain. That is to say, it should increase the total you have to use but when you lose the trophy, the awarded extra points do not go away until the overnight reset happens.
So if you gain a training trophy, you get an additional 5 training pts to use immediately after the battle. The next day, if you still have the trophy, you have 15 to use for the day. However, if that 15 is not used up and the trophy is lost in the next team battle, you should still have 15 to use not 10 until the next reset. The next day you should just have 10 pts to use.
The same goes for the energy and courage trophies.
When you win extra points from defeating a villain, the extra points stay with you until the next reset. They don't disappear if another villain shows up before the next reset. So why is it different for a villain battle and a team battle? I don't think it should be,
