The app is saving them in a folder that doesn't have a .nomedia file (which prevents the folder from being scanned). Find the folder the files are in (with a file manager) and create a file named .nomedia (nothing to the left of the dot - the dot is the first character). It doesn't matter what's in the file - even nothing - it's the fact that there's a file there with that name that does it.
Welcome to Android Central! Are you sure it's not just thumbnails that the system is saving? It's normal for devices to save thumbnails of images temporarily. If you happen to connect the device to your computer via USB and select the Import Photos option in Windows Explorer, you might see all of those images (in thumbnail form) appear on your computer, because the Import Photos option indiscriminately copies over every single image on the phone.