Ran into this myself and was going to report it. I'd like it to be fixed properly though and it's in your interest! I'm the Gentoo Linux games team lead and I'd like to add this game to our repository. This would give you added exposure. It would be involve users downloading the purchased zip from here, sticking it in a folder, and the package manager would install it system wide with a menu icon and so on. That doesn't work when the save data is written to the system-wide location. Where should it go? There are already a couple of files, prefs and Player.log, written to ~/.config/unity3d/ChrisChung/Catlateral Damage, and it should live alongside these. I had the same issue with Assault Android Cactus+, which is also Unity-based, and they were kind enough to fix it for me. Please could you do the same?
P.S. Thanks for keeping my daughter entertained for an afternoon!