He took off his shoes not to be polite but because if he didn't then he'd leave dirty footprint marks all over the floor which will easily alarm the household members that someone else broke in.
To be honest, this is one of those rare situations where I wouldn't give a cent about the story on Chapter 1, and instead now I'm completely hooked, hope this keeps up!
@cgr oh yeah that's definitely why he took his shoes off, it's just that my first thought was "wow he even brought his shoes with him instead of leaving them at the door" until I realised how silly that was.