Death of students in various academy would be investigated, and with the assistance of the badge, it was easier to investigate.
But things are different outside the academy. They were all on a mission to assist the army in eliminating the dimensional beasts.
For the average first year student, this mission wasn't particularly easy, but it wasn't so difficult either.
However, this city has been over run by titan and even gigantic beast, if one wasn't particular careful, one could lose their life without having any idea how they even died in the fist place.
Killing the student might be uncalled for, but along with his bad mood, the student actually had killing intent towards him.
Moreover, he was also heading towards the mansion. It was obvious he was well aware that there were treasures there. If Tyrion had let him go, he would group up with others and look for him or spread the information out since he couldn't gain anything from it.