We've encountered this problem on a previous project I was on, a big banking application.
For added security we made the app to automatically log-out after five minutes of inactivity. We found it disturbing for the user that Android OS would still show your personal account info in the Recent Apps overview. This would be visible until you really closed the app, rebooted your Android or returned to the app and exited it on a screen without any banking info.
After quite some research we found out that Android (since ICS, so Android 4.0 and up) is using the internal screenshot feature to capture the screen for use in Recent Apps. There seemed to be no user option available to prevent this, only the developer of an app can restrict this.
You can ask the devs of ZDbox to include this feature in their app or options by contacting them at firstname.lastname@example.org
Just a heads-up: If a dev does this, then the screenshot goes full black. We decided to offer a placeholder image instead, so it doesn't look bugged to the average user, see bottom app in screenshot below.
Hope this info is still usefull to you! :)