After you play the Serving Game with Kate, listen to her conversation with Thomas at midnight.
If she didn't earn enough, you can pay money to Thomas in her place.
If you decide not to pay or you don't have enough money Thomas start to make moves at her.
When Kate has 20 Affection Points you can make Thomas stop hitting on her. The next time you talk to Thomas he propose to let him scold Kate again in exchange for a free room.
If you accepts the free room or you let his conversation with Kate reach the point where they kiss before making him stop, the NTR path is set (they will end up having sex) and Kate will give the Soldiers Handjobs when her Corruption is high enough.
