The reputation and customer confidence in Kucoin will have dropped a lot no doubt.
Back then, Binance was able to quickly recover the losses that occurred due to hack I think that's the reason their reputation was intact. I think It will all depend on how quickly KuCoin will act to reimburse the users who lost $$ during the Kucoin hack.
They guarantee that they will reimburse the hack funds, did we see any problem already regarding their promise, do people complain about their funds not reimbursed by Kucoin? If they won't reimburse, that, we can say that it will affect their reputation which I doubt they'll allow that to happen.
They are definitely going to reimburse, but they need to do that quickly to save their reputation in the crypto industry because you know the more time they take the more time FUDDERS will have to spread FUD (IMO). I have seen so many exchanges got shut down after they suffered a hack hopefully the same will not happen to KuCoin.