Prediction: I think the check-up event will be the start of the Dante training arc.
The last section of the trailer where we go through a room of Peccatula I think hints at that as part of the check-up Dante will be sent to fight them without the sinners (maybe even without any weapon) and will get the shit beat out of them. This will then result in Dante starting to learn how to actually defend themselfs at least against weaker threats either of their own volition or cause Limbus forces them to.
