There's blood residue in places, but we don't know if it's human or animal blood. Did the police look into that? Whose blood is it? If the answer to these is classified, then knowing whether it was found in rooms where he went while he was with the police would mean that it is probably the dead thief's blood. Since he had been dragging the body and not carrying it, it wouldn't be unreasonable to think he only got a small amount of blood on his shoes/boots and, unless he had stepped on puddles of the stuff, forensics would only find residue of it and not actual footprints. Which means there would be no reason to try to scrub it off and so we don't have to factor that into the timeline.

......Unless it's the wife's blood and Endre walked through these specific rooms on purpose to make police assume it was the thief's and so not look too closely at it. I mean, they're perfectly happy letting him keep his gun, so it wouldn't surprise me.