If the butler had come in through the front door as he said he did, there would have been mud foot-tracks in the entrance hall on the Persian carpet (It had been raining).

The Persian carpet would have no longer been immaculate. But remember, the Persian carpet was immaculate, completely clean, before Policeman Peter wiped his muddy feet on it upon entering.

Benny the Butler is lying… And he has no reason to lie unless he is trying to hide something in the middle of a murder case.