How do I figure out which file is the loader background image?

Download a mod manager. I have the one by GametimeDev!

Interesting. I'm cautious because viruses regarding mod manager.

citymajor​ They're all .package files. Many creators will put some variation on "loading screen" in their filename, though. 

You could try an internet search by image, but it might just turn up whichever site the person making the mod took that from, though. It's unfortunately very common that people are posting stuff they didn't make themselves for loading screens.

I did search through The Sims Resource and found it, then downloaded it and checked the name. Searched for the same in the mods folder and removed it. Magic!