How to block updating the client?

Any older TeamSpeak 3 version, It'll constantly ask to update, because the checks are hardcoded, even if you delete update.exe or block it, still will check for updates. What you have to do is go to this directory:

On Windows: %WINDIR%/System32/drivers/etc
On Linux: /etc

And find a file called hosts. Open the hosts.file and add these lines:

127.0.0.1 versions.teamspeak.com
127.0.0.1 files.teamspeak-services.com

So now every time TeamSpeak 3 check for updates it will fail, since it will check for the local IP, instead of main domain. Since the server won't be located locally, it will fail the check every time. In case you still want to update TeamSpeak 3, then just delete these lines or download the new client and update it manually. (Keep in mind the latest version of TeamSpeak 3 v. 3.6.2 is only compatible with Windows 7 and beyond and thus It's not compatible with this server)

Note: For systems like Windows XP/Vista it might require access to Safe mode, before any modification in the hosts.file.