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They obviously do not belong in the house.
If the house is built correctly, they can’t get in.
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We had a VERY bad year for rats a couple of years ago. They were literally running on the roads at night. The old adage “if you don’t see any, you’ve got ten, if you see one you’ve got 100” was an understatement. My whole neighbourhood had them in the houses, in the trees, in the woods, in the RV park, in the HOSPITAL (1/2 mile away), everywhere. This year it’s not so bad, I have eliminated only 5 in the last 2 months.
The squirrels chewed their way through the fascia boards between the eavestroughs and the shingles’ dripline. They were using the stucco on the south wall as a raceway.
My mail carrier thought I was kidding him until he saw it with his own eyes.
I don’t care how poorly built you think my house is (built in 1964, has survived several earthquakes, dozens of serious windstorms of 50+mph, and a blizzard that dropped 4’ of snow in 30 hours), they would have gotten in your house too, I guarantee.
Unless your cat has access to the attic... < BG >