The prompt message that you're getting is to authorize QuickBooks with "Full account access" for your webmail provider.
Please know that the QuickBooks Webmail feature is following the OAuth protocol. This protocol is an open standard for access delegation and used by some companies, such as Google, to permit the users to share information about your account with third-party applications or websites.
To connect your Gmail with QuickBooks Desktop, enable the 2-Step verification first by following these steps:
Click to enable the 2-Step Verification and enter your phone number under Voice or TextMessage. This will be used to receive a numeric codes from Gmail, which is needed to authorize access to other third-part apps.
Choose Send Code.
Enter the verification code send from Google and click on Done.
Follow the on-screen instructions to successfully enable the 2-Step Verification process.