bro, I think it's more of their reputation at this point. ch13, he clearly thought that her behavior is unfitting for a noble, for now it's okay only cuz she's a kid but he still think it's wrong.
So if she got caught cheating on a test, in a mostly noble school with others who are the norm of nobles or better doing the test normally. it would shame them greatly as to say that she is worst then all of them since she even has to Resor to cheating and even dumber to be have gotten caught doing so.
smacking their faces because they 'raised' her, given her 'education' and is her parent.
forgot to add, that there is commoners in there too who gotten in for talent/smarts(scholarships).
So if they clearly didn't cheat or is smart enough to have not be caught doing so. SHE, as their daughter, is worst then a commoner that is lower status and can't even eat with them without it being short show. ┑(￣Д ￣)┍
I think his parents are so strange in the way they were like “if you ever committed crime, I will not hesitate to throw you away” like that’s an insane thing to say to a child