Re: Restoring saved games after reinstall
If you have already deleted the game from your device, then the only way I know of on how you can restore your saved game data is as what JustMe'D posted that the game should have supported/synced your data to iCloud.
Now, for games that don't support game data sync to iCloud, I use iFunBox to keep a backup of my save game data to my PC. That way even after I have uninstalled the game, I still have a copy of my saved data should I wish to play it again after some time and continue from where I left off of my previous save. Though for this to work, you need to backup your save first before uninstalling the game on your device. And I know that this won't really help you with your current situation but maybe this could be of some use to you should you want to keep a backup your other saved game files.
Here's what I do:
STEP 1: Download and install iFunBox latest version
STEP 2: Connect your iPhone (iPad) to PC. iFunBox should now detect your device and display it on the program screen
STEP 3: Click on “User Applications”.
STEP 4: Scroll down and select the app you'd like to make a backup file of. Click on +.
STEP 5: Select both Documents & Library. Right click then select Copy to PC. Then just choose which folder directory you're going to save it to.
That's it. For transferring the save back to your iPhone or iPad, just follow the same steps but instead of copying to PC, you need to choose "Import to device". And please note this may not work with some apps.