How can I run TntConnect on my Linux?
Step 1) Install CrossOver Linux.
This CodeWeavers tutorial has many helpful tips:
How to install CrossOver Linux
Step 2) Download and open (double-click on) this file:
TntConnect-on-CrossOver.tie
Step 3) Click "Load" when prompted to load untrusted CrossTie file.
(Note: "untrusted" simply means that CodeWeavers didn't provide the file.)

Step 4) Click "Install" when prompted that CrossOver is ready to install.

Step 5) Follow all the normal prompts to install software...
(Note: If the installation never starts, you may need to get tech support from CodeWeavers.)

Any final hints?
CodeWeavers has many helpful tutorials here: CrossOver Linux Tutorials