Dunno if it will help you any now, but this is my experience. The bank I use had put out an iPhone app that I was comfortable with and used periodically. Installed it and, in due course, sync'ed the phone with iTunes to local storage on my Mac. All was good.
Then the bank put out an update that was, in my view, a regression and posed a security risk. Found this out after updating OTA and testing it. Since I did not want that version, deleted it on the phone. All through this, the phone was not sync'ed on the Mac, and I don't use iCloud nor have automatic Wi-Fi backup enabled. Later, when I did plug the phone to the Mac and sync'ed, the computer still had the previous and desirable version of the bank's app. So I just reinstalled it with the corresponding button on the phone's Apps pane in iTunes and all was good again.
Now I have to be careful not to do an Update all either on iTunes or on the iPhone's App Store application to ensure the older and acceptable version does not get replaced.