Bismillah

Al-Jawab Billahi At-Taufeeq (the answer with Allah's guidance)



Yes, it is permissible to kill such pests.

Also, to kill animals and insects which are harmful to one's self is permissible. However, to make the animals etc, suffer is forbidden.

Abu Hurayra related that, "The Messenger of Allah (Sallallahu Alaihi Wasallam) forbade making animals suffer." (Bukhari)



And Only Allah Ta'ala Knows Best.