I appreciate you for sharing the error message your bookkeeper has encountered, @Scribbler.
QuickBooks Desktop (QBDT) will only access a website that is related to QuickBooks. You'll want to make sure your QBDT is up-to-date with the latest features and fixes to isolate this issue. Let me show you how.
- Go to the Help menu and select Update QuickBooks Desktop.
- Click the Update Now tab.
- Select Get Updates to start the download.
- When the download finishes, restart QuickBooks and accept the option to install the new release when prompted.
If the issue persists, I recommend reviewing your Internet Explorer settings and ensuring it's configured to Use TLS 1.2. You can refer to this article for the detailed steps: Get help with errors 12002, 12007, 12009, 12029, and 12031 when updating.
Once everything is in place, you can utilize this link for reference in seamlessly matching your accounts: Reconcile an account in QuickBooks Desktop.
I'll be around if you have other follow-up questions running your QBDT and managing your accounts. Keep me in the loop by leaving the details in your reply. Take care and have a great weekend!