They can climb anywhere they want. I moved out of a house in the country where I never won my war with them. And yes, I killed them and never felt bad. I had 4 cats and a dog that would get them daily, but I always had more. I counted 17 killed in a couple of months from my pantry alone. They did not get into any food because I had it all protected. They would get into a cupboard I had and leave their calling card on my dishes. And if you have a gas oven, don't store your pans in there because they will get in there when it is cold. I had to set traps on top of my stove every night and sterilize it the next morning.