Teamviewer does NOT support taking screenshots or remote control
The only Android devices it does manage to pull this off is on Samsung
This Teamviewer press release shows how it's done. It
basically installs this Samsung specific addon from the Play Store. As a
background, Samsung got this working to counter Amazon's Kindle Fire's new feature called Mayday.
Technically, Samsung basically gave Teamviewer a bunch of special
pseudo-root-level certificates and signatures so the app can work
seamlessly for everyone.
This is how it looks on non-Samsung non-rooted devices
[left] and how it asks for Super User access on
non-Samsung rooted devices [right] (Click through for original