I've talked with the translator, "advenge" was a typo. The actual word was supposed to be "avenge". So the girl Otoya killed was the person Shiena needed to avenge. But since she is now dead, Shiena is freed from her debt, since this girl probably had already avenged her. This is why Shiena "owes" a favor to Otoya.
This is also probably why Shiena went to Class Black. Since she can't repay her group, she decided to try to get a wish for them.