I don't know...
I've been vegetarian my entire life, so I know for an absolute fact that humans do not need to eat animals in order to be in good health and lead happy fulfilling lives.
And, I don't see any way in which a death trap would be any more effective than a live trap, followed by removing the living "pest" to a more suitable habitat.
Besides for which, I don't know of any actual evidence that mice are a health or construction hazard (although feel free to educate me otherwise)
Without either of those, I think AJ may be right - we don't like insects and rodents in our homes just because they are creepy or annoying or ugly or whatever. Is a mouse any dirtier or more filled with germs than a dog or cat? Probably not.
For that matter, is a dog or cat any more or less conscious or intelligent than a cow or a pig? From what I hear, pigs are actually smarter than either of them.
I don't think we get to have it both ways - either unnecessary killing is wrong, or it isn't. If we are willing to mentally justify it to ourselves when we have a reason to prefer it, how can we judge others for making that same choice, when they are valuing cold hard cash instead of a tasty meal or a "pest" free home.
Like I said, I've never eaten an animal in my life. I have a good friend who has pet rats which I've hung out with before, and they are pretty cool. And I generally either carefully remove insects from the house intact and alive, or I just let them live here (esp spiders, since they catch the flys and I can't stand the sound the flys make)... and yet, I don't really see the moral outrage of this psychology experiment.