Apps do have to go through an approval process to be on the Android Store (Google Play) or the Apple Store/iTunes. If anyone is an app developer, you will know that even the simplest apps go through this process and are tested just as thoroughly by Google and Apple.
If there was anything dodgy going on that wasn't part of the app specifications then it would be shown up in that process. There are far more malocious people than the WTBTS who would love to create apps to spy on you and steal your data, so Google and Apple have to have a pretty rigorous process to stop that.
The worst I can imagine the WTBTS doing is storing the ID and/or location of your phone against a database of any searches you make on the online library, but even that would require way too much computing power and storage space to justify what could be done with that info.