Background check - quit internship early

Hi! I would really appreciate advice/thoughts on a situation that is giving me some sweats.

- I applied to BB internships for spring/summer 22 and had an incoming internship at bank A (for fall 21) on my CV. This inc. experience was very briefly discussed during interviews

- I have now had to quit the internship early due to urgent family issues

- Bank A was understanding about my situation and wants to defer the internship with start in 22 instead and they want me to sign this immediately

- I however want to accept an offer from one of those other places as this would be much more in line with my long-term career goals and really valuable to me

My worries are:

(1) Will quitting early be an issue in the BC? Should I inform HR at the new place in advance?

(2) I would prefer to reject the extension/deference of my offer from bank A without saying that I will be going elsewhere because it might lead them to doubt the seriousness/honesty about my reasons for leaving early (I have been 100% truthful but they can obviously not know for sure). But, they will eventually receive a BC phone call and find out -- should I tell them now or wait until just before the BC, letting some time pass?

Thankful for any input!