What you do, if you want to do it cleanly, is "reconcile" the credit card account to your paper statement. Quicken will prompt you for summary charges and credits that will also be in the bill. At the end, if you owe something (likely), it'll then prompt you to write a check for the correct amount to the credit card company.
When the check clears it'll show up as a transfer: A debit in your checking account (that's right, you just paid out the cash!) and a credit in your charge card account, making the big negative balance smaller (also correct).
With Discover, sometimes the closing date on the statement doesn't quite match up with the posting dates of some of the charges, so, during reconcile, one might have to uncheck a couple of the latter transactions, then make sure to check them, again, the next month when they do show. But that's a minor quibble.
Ken Becker