Given the average monster size, I am not surprised the exterminators refuse to kill the monsters. You should call the military instead. XD
But yeah seriously, maybe exterminators should just refuse requests if enemies or monsters are on board. Instead add a new (more expensive) option requiring a military airport to have military forces search the ship, eliminating monsters and other enemies. Could be so that they only eliminate their enemies, so if you are docked at a netual 3rd party city, they won't remove the troops belonging to your enemy if they aren't their enemy too.
But yeah seriously, maybe exterminators should just refuse requests if enemies or monsters are on board. Instead add a new (more expensive) option requiring a military airport to have military forces search the ship, eliminating monsters and other enemies. Could be so that they only eliminate their enemies, so if you are docked at a netual 3rd party city, they won't remove the troops belonging to your enemy if they aren't their enemy too.