Killing the Clacking Centipede had been the end-goal for the Beast even before the corruption.
Lea Gilligan was a Beast expert and part of that was knowing that not all Beasts can be pacified without killing. Not all Beasts can be 'reasoned' with.
Nature operates on a balance and for every terrifying-looking creature with a soft side—like the Bulcroc—there is also a terrifying-looking creature whose entire reason to exist is to kill. Hell, there are some cute and cuddly ones who would kill if given the chance just as there are those who just want to be loved.
Suffice to say, the Clacking Centipede was meant to be stumbled upon and then killed to teach this message to the students who happen upon its 'habitat'. As such, Lea didn't mind that the Beast had been slain. She did mind though that the uneasy feeling in her chest had yet to go away.
