How to Remove Devices from the List of iMessage Text Forwarding

After selling my iMac and buying a MacBook Pro recently, I was left with the iMac as a device on my iPhone to forward  text messages in iMessage. I could turn it off, but I couldn’t find a way to remove it from the list of devices.

I tried signing out of iCloud and deleting the device from the web interface of iCloud, but neither resolved my issue.  After searching Google (as one does) I found an article from MacWorld by Glenn Fleishman.  It required changing your iCloud (or Apple ID) password.

But there’s an answer, found in discussions online among users with similar troubles: Change your Apple ID password, and the phantom devices disappear. Whether you’re using password-only, two-step verification, or two-factor authentication with your Apple ID, changing the password can mean re-entering it and going through a code-based verification step in a lot of places. But it will also solve this problem.

The answer is quite easy, but not well thought out by Apple.  It is actually rather annoying to have to change a password to remove a device.  I hope a future update corrects the oversight by Apple.