The app has been unlisted from the problematic countries. The installs are not coming from the Play Store but rather somehow the APK is being installed directly to the phones. I don't know of a way to block this from occurring.

Block them from the backend of your app, ie, your server, using IP geolocation techniques.

We're prepared to do this if necessary, but most of these users aren't actually using the app. So the only apparent damage is them getting upset that the app keeps reappearing on their phone.

If that’s what’s happening and it’s not happening through the play store then I’m afraid there may be nothing you can do about it.