Hi Mark_R
Thank you. The messages in the Items Received section do not contain any transactions- they are just communications about things like my user name. The only place where this transaction is visible is in my downloaded transactions window after I press View in the Bank Feeds window. It's not possible to use the delete button in that window to delete the transaction. I'm still stuck.
It seems that you're using Classic Mode, @ckrash. That's why you don't see the Transaction List button.
I'll walk you through the steps to change your bank feeds mode. Thus, you can remove the 2015 transactions from your QuickBooks Desktop (QBDT).
QBDT offers three banking options: Advanced, Express, and Classic. The Transaction List tab is available in the Express Mode. To change the setup, follow the steps below:
- Go to the Banking menu and select Bank Feeds.
- Click the Change Bank Feeds Mode tab.
- Choose Express Mode and click OK.

For more information, see this link: Switch between banking modes.
After that, follow the instructions outlined by KurtKyle_M above to remove the old transactions. For further visual references, see the screenshots below:

Furthermore, see the following articles for information on how to bulk delete transactions and reconcile bank accounts in QuickBooks:
Drop me a line if you need help managing your bank transactions. I'm happy to assist again. Take care!