Having been in that position before, I’d recommend you be reasonable. If delaying occupancy a few days is not a big deal for you, then figure what reasonable rent for the few days would be, and allow it. To be safe, you might want to include some sort of damage deposit, but remember, these are the people that have been living in the house. The likelihood that they’ll change their lifestyle, and do a lot of damage, because you did them a favor is pretty slim.

Shit happens. Maybe the place they were planning on moving into won’t be ready. Maybe they have some sort of family emergency. There’s no reason to bend over backwards for them. But neither is there cause for you to make their lives miserable, just because you can.

And yes, of course it’s legal. They would like to rent it back from you for a few days. It may be a perfectly logical request. You don’t have to do it. You’re free to be an asshole.