"Unrooting" means deleting a file named su. That's it. If anything was done to the phone when it was rooted, that can't be done if it's not rooted, what the app is detecting is "this phone was once rooted". And some apps are written to not run in that case.
To totally
unroot the phone, you'll have to reflash the stock ROM. That means backing
everything up (see
Backing up an Android Device), flashing the stock ROM, then restoring everything you've backed up. (Some things are already backed up - they're in the article.)