He doesn't abuse the time she gives him too much. Although he doesn't tear through the house in a flurry of trying to get everything sorted in a hurry, he isn't as methodical with his approach as he would have maybe liked. He has to double back a few times, make two trips when he ordinarily would have only needed one, but eventually it'll be as tidy as he can manage. He also makes sure to disable the most fatal booby traps around the house and keeps his paranoia confined to just the basement door and the back door like he promised.

While he doesn't feel comfortable going through her clothes, he will bring the towel as promised. He doesn't rush her to finish up her shower though, placing the towel down just outside the bathroom door.

He's probably overthinking things. Or stressing out about this sudden new arrangement more than he needs to. In time he'll settle down. Might even get comfortable with someone else to share this big old empty house with. The fact that she doesn't talk should suit him but he might find her silence a little disconcerting at first.