The app in question is iCare by Chen Yuhua. I have tried uninstalling the proper way through launchpad and also manually by removing all files and system files that are returned by Searching "iCare" and "Yuhua".
In both cases, the app immediately reappears in the updates tab of the Mac App Store. The developer told me that the problem is with the store, not his app.
So, how can I permanently remove it so that it doesn't reinstall itself?