How can I see (and delete) app data for apps that aren't installed? I recently did a "restore" of my iPhone, and loaded data in from a backup (an iTunes backup, not iCloud) So, all my apps were gone- I had to re-download them. So I did, but I noticed that when I did so, the data was all still there.

However, I didn't (and don't want to) reload all the apps I had installed. So, what I want to do is be able to see which other "not currently installed" apps have data on the device, and be able to delete some of them. How do I do this? 

(Or, was it actually just pulling this data from iCloud, despite that I was using an iTunes backup?)
Yes, you're just syncing the App's data with iCloud, as no files are leftover when an App is deleted. 

iOS apps (and now  OS X  apps too), are Sandboxed. This means that each App has its own space in disk, with its own directories, which act as the home for the App and its data.Deleting an app from the iPhone deletes this sandbox, deleting all data associated with the App.

So, if an App supports iCloud sync, whenever you install that App with your Apple ID, in any of your devices, all the information will be synced.