Minecraft chat sometimes contains 't' when opened on Linux?

I think that maybe your chat key gets stuck a bit and enters 2 "T's" into the game. If you want to, you can rebind the Open Chat key or you can just delete the T. Hopefully its because of the T key and not the game

Adjust the speed that keys get repeated

What could be happening, is that your operating system is detecting a "Key held down" event - and thus starts repeating that key before you release your finger, inserting a t (or whatever character you set your keybind to in Minecraft) into the chat box.

Given that you say this only happens 'sometimes', you're probably pressing the key just the right amount of time to start the repetition, meaning you should only need to adjust it slightly for it to not repeat on you.

Ubuntu

Change/Adjust the 'Repeat Keys' setting. From this Ubuntu help page:

1. Open the Activities overview and start typing Settings.
2. Click on Settings.
3. Click Universal Access in the sidebar to open the panel.
4. Press Repeat Keys in the Typing section.
5. Switch the Repeat Keys switch to off.
   Alternatively, adjust the Delay slider to control how long you have to hold a key down to begin repeating it, and adjust the Speed slider to control how quickly key presses repeat.

ArchLinux

This can be achieved by adjusting the 'typematic delay' settings, using the command kbdrate. From the ArchLinux wiki:

The typematic delay indicates the amount of time (typically in milliseconds) a key needs to be pressed and held in order for the repeating process to begin. After the repeating process has been triggered, the character will be repeated with a certain frequency (usually given in Hz) specified by the typematic rate. These values can be changed using the kbdrate command. Note that these settings are configured separately for the virtual console and for Xorg.

# kbdrate [-d delay] [-r rate]

For example to set a typematic delay to 200ms and a typematic rate to 30Hz, use the following command:

# kbdrate -d 200 -r 30

Issuing the command without specifying the delay and rate will reset the typematic values to their respective defaults; a delay of 250ms and a rate of 11Hz:

# kbdrate