@huttingham
It would be okay if they did the body check in more appropriate place but in the meeting hall with all other people there, not to mention men too, is seen as act of "humiliating" the princess. Of course the bodyguard got angry as her princess is shit upon, she can't let her boss dignity be pissed upon like that.
If the princess party just accept, it would be make them appear as "inferior" to the mc party, meaning they would have less disadvantages (added with the ones they already have) in negotiating with the mc kingdom in the future.
Yeah, sure, you see this is as a stupid scene But all these pretense are important to show the characters are not just flesh bags.
As for why MC don't act, well he already agreed to the queen to let that duke son do the job and everyone knew that. if he interfere, it could be seen that he cannot be controlled by the queen or their relationship is not really close or any other negative implications. Any of that could be use by the politic players to usurp more power for themselves within the kingdom.