Curious...
Does Uber show up in the Application manager if you select the 3 dots at the top right, and then select "Show System"... this should reveal all the hidden apps, that run in the background. Be careful in here, there are system-critical apps running that could bootloop your phone if you kill the wrong process.
If it does, you need to select the uber app:
STORAGE =>Clear Cache => Clear data
Force stop => Disable (or Uninstall, if ATT allows it)
If you don't do it in that order, it may not fully un-install.
Furthermore, I recently found that may not completely omit everything from the app. I have had to then go into file manager and manually delete sub folders for those apps. I found remnant storage folders from Chomp SMS and Real-player, I deleted these over a year ago. They had zip files and other "system looking file types" in there. I am not sure what they were, but I absolutely did not want them on my phone.
FWIW I am on Verizon, not exactly the same bloat as ATT. Hopefully ATT allows it to be deactivated or uninstalled. Greenify does work for a lot of these kinds of things. I used it for a little while too. But IMHO its kind of like a band-aid. If you can cure the problem using application manager in the OS, that's better.
Good Luck!!!