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?)