The core charge is a refund the parts store chooses to give to you, it is not a discounted price, you will never find anyone who gives tax back.
I sell car parts for a living.
Chinese parts are cheaper due to cheap labor, not due to poor craftsmanship.
As mentioned, Honda CV's have several variants with little or no way to decide which one is the next one.
Also as mentioned, either bring the core to match it up, or wait until the job is done to return the core. In my experience, remanufactured anything is less reliable, especially CV's, alternators, etc, reuse the old housing, and just replace the electronics, thus the lower price and the higher reliability (Nastra, for instance, has a lifetime warranty on all new and reman parts"