When parents ask me, I let them know that according to state regulation, they can drop in at any time and that I will always welcome them at any time. I explain some of the drawbacks of stopping by at certain times of the day (like nap time) and then leaving without their child but then restate that I want them to always feel comfortable to come by at any time. I then talk about the importance of open communication between us and encourage them to talk to me about any concerns they may have.
To be honest, I can't stand it when people drop by. Not because I'm trying to hide anything but I just don't like feeling as though I'm being watched and judged. I think the fact that I stress that they're welcome to stop by at any time makes them feel as if they don't have to. In 21 years of doing dc, I've only ever had one parent (and several members of her family!
) feel as though they needed to drop in to try to "catch" me doing something wrong.