I heard one local exchange like this from our exchange, like if your outgoing transaction is worth more than $900 USD, they are asking for some information and putting the transfer on hold, like some information about who the receiver is, etc. I haven't tried this yet, but more likely the same with your case.
I think using an intermediary wallet that you own is a good idea as long as they have already sent it, and they are already safe, but your account could be in danger if they still care on the funds after you transfer it out from the intermediary wallet.
I only think of concern about origin of your deposit fund that is more important for centralized exchange to have good AML enforcement on their exchanges.
They only need to consider about a withdrawal if a receiving address is well known as from a mixer, that is the only case I think possible for triggering their AML bot with withdrawal. For withdrawals to non minder addresses or non sanctioned address, there is no reason for asking such question rather than intention to scam users through AML card.