Killing the bent-four-in-the-corner should come after filling dames (to remove outside liberties) and removing ko threats. If there are unremoveable ko threats, then whether or not one should try to capture the bent-four-in-the-corner will depend on strategic considerations.
Also, without unremovable ko threats involved, I think most reasonable players would simply just accept that the bent-four-in-the-corner is dead without having to play it out.
https://senseis.xmp.net/?TerritoryScoringVersusAreaScoring#toc7
It affects how you should play endgame half point Kos. P.S. I doubt most of my real life opponents knew this (we use Chinese).
As a follow-up to this point, I made another forum post going through a life and death example under Chinese rules:
The difference between those two counting methods?
I learned the hard way that the score estimator is based on Chinese rules. Score estimator showed +0.5 for Black. After we both passed I lost the game with -0.5 points. 
Let’s ponder that by a bit of luck factor (at our level)
That’s understood.