Disable dismissing reminders from lock screen Can I prevent Reminders from being dismissed on the lock screen? I do want Reminder to pop up while the phone is locked. I do not want any random person to mark them as completed while the phone is locked.

iOS 6 would display the reminder, but required the passcode to dismiss it. Can I do the same in iOS 7?
Try Settings > Notification Center > Reminders (second entry - with apps) > Show in Notification Center and Show on Lock Screen. Also choose whether you want "banner" or "alert" style notifications.

There is a third Reminders setting on the main settings page, but that only relates to how long you keep old reminders around, and which list of reminders you want to use. HTH