Log in to your Checkbook.io account.
If you have only received a check and not created an account, use this link and click "Forgot password" to set a password to the account that was automatically created for you with the email that you received the check on.
Go to "Settings" on the bottom left-hand side of the page.
When in Settings, click on the "Accounts and Cards" tab.
Once you reach accounts, you will see your banks under the Bank Accounts tab - Select the bank you want to delete and click on the "Delete" button.
NOTE: The Default account may not be deleted. So in order to delete, you will have to add another bank.