That is true with almost all applications in the Ubuntu repositories: They lag behind in their versions. The reason is that Canonical usually checks the packages for security and compatibility with Ubuntu. Also someone has to build the .deb package and upload it to the repository. That adds an extra step and slows things down but increases the quality and feel of Ubuntu.
That being said, you can't update the main repository. All you can do is create your own ppa on launchpad and hope people use it. Lauchpad has good introductory guides on how to do that. You could also get in touch with Canonical and propose your new build.
If you want to "update"
TTYtter only locally on your system, you're free to do so but the next update in the main repositories might override your changes with yet another outdated version (which might break your configuration). To prevent that you should put updating on hold
sudo aptitude hold ttytter (more info).