I see, in the meantime, you can prevent them from downloading apps:
Settings>General>Restrictions>
"Enable Restrictions" (be sure they don't see you enter passcode). Then, under "ALLOW" turn off: "Installing Apps", "Deleting Apps", "In-App Purchases", perhaps also "iTunes Store" to prevent them buying music/TV/Movies and "iBooks Store" if any of them might get a book. I did this and the App store disappeared from my home screen. You can just come back here to turn back on when you need or this is fixed. The passcode you set for "Enable Restrictions" will be needed to turn these back on. If you need to change the passcode here, just "Disable Restrictions" then enable them again and it will ask for you to enter a new passcode.
I updated to 7.0.3, but this bug still exists. The same bug exists on my old iPhone 5 that my wife is using as well. Very strange that I've not heard anything about it from anywhere else. Seems like a pretty big bug.