how do you download recent transactions in current month from apple to quicken?

Fees could be one hurdle, but the Apple Card website is barebones. Apple probably wants integration into iPhone and limited internet integration. iPhone is a required device and Apple wants a co-branded card to reinforce that integration.

Quicken would need to go the iPhone route to gain access. Then there is the fee issue, that Apple probably wants a part of.

That’s not a service that’s currently supported. Downloadable transactions are available for prior months only.

Download or export your Apple Card statements and transactions - Apple Support

The iPhone app Mint supports that function. I believe the website route is not being supported due to security concerns.