There are a couple of options that you have depending on what you want to do.
If you want to control the desktop of the TLA from your Linux box, it is suggested that you use VNC. This can be found at http://www.realvnc.com/ .
If you want to automate control of the TLA from your Linux box, you need to use either the .NET interface (TPI) or the COM/DCOM interface (TPI.NET). Active Pearl is COM enabled so this would probably be your best bet. Mono is an open source project that will allow you to use the .NET interface.
TPI.NET is only available on TLA Application Software v4.3 and above.