If both your bank and credit card accounts are connected to QBO it is best to make a bank transfer from the bank to the credit card account, then match the transferred payment within the credit card account bank feed. Do not enter bills for your credit card statement and do bill payments. If you just wrote a check, make sure that the account you selected for the check payment is the credit card account. When this check payment comes through your bank feed you can simply add or transfer the payment to the credit card account and then match the added or transferred payment received within the bank feed of your "connected" credit card account.
You enter a check expense and the entry for the spending detail is the CC account, because you just paid down that debt balance. This is not when you paid for office supplies; the office supplies were paid for when you used the card and that spending should have already been entered as a credit card charge for the date you bought the supplies and for the party you bought from.