What's this part called? (a manual transmission shifting mechanism connecting to the shifter under the hood. 2000 hyundai accent)

Close up of it.

Zoomed out, to show it’s relative location.

Awhile back, I was trying to see what I could do to improve the feel of the shifter, and decided to proactively replace the gear oil and lubricate whatever I could. Replacing the gear oil didn’t affect this much (I’m a newb. I don’t know), but I did end up spraying down the part in the first image with WD-40 and the shifter improved right away, but temporarily.

What is that part called?

(bonus question: Any thoughts how how to improve my shifter?)