Originally, the idea had been to give it to Malfoy for these sessions and to take it back, so that evidence wouldn't be found on either of their wands. Originally. But the look on Malfoy's face made Harry hesitate. Why did he need to take it back? Did he not trust Draco with an unregistered wand? If he was going to be trusting him with his mind, Harry realised, it would be stupid not to trust him with everything else.
"Yes. You can keep it. Just don't bring it with you to the Ministry," he said, ever the master of stating the obvious.