Lady Grey is a Noble Woman, who you can occasionally meet in a daily event if your Naginata Skill is above 30.
If you refuse the duel, your Renown decreases.
If you accept, then your Renown, your attack and defence skills increase (win or lose). You also win or lose 20 personal gold as a bet. If your fighting skill is already at 100 points, when you win, you'll get a bonus, boosting your skill past the limit.
Then the loser has to serve the winner. In case Lady Grey wins, in a day or two she will send her sister to tell you to meet her at the Onsen. You have to personally supervise your slave for that job. If you miss the appointment, then her sister will inform you that Lady Grey will never see you again. If you go, then Lady Grey will have you act as her attendant.
If you win, Lady Grey will offer you several possible services. If you choose an intimate service, then the next time that you face her, she will be harder to beat.
If you manage to beat her 5 times in a row, or a total of 10 times, she will come to challenge you to a final match. After winning this match, Lady Grey will become a Minor Slave. However, her standing towards you can differ, depending on your interactions with her before this final duel and includes her becoming an abused, mindcontrolled or tentacle-raped sex-pet, you becoming her 'submissive' and her becoming your wife.