The email pdf is definitely not new.

As to the card, I’ve been asked about that for ages. I have 2 on my profile. It makes a difference for insurance and foreign exchange which one I use. I’m careful to select the one I want when I reserve. I double check they have it right when I pick up. I am pretty sure the agent at drop off routinely asks “do you want to keep it on this card”.

I particularly check the card if it’s a longer rental (more than a month) because they will automatically put the charge thru.