Hello,
You can't erase messages directly from the Phone Link app on your PC because it is meant to reflect messages that are already on your phone. "Ghost" copies of the messages you see in Phone Link but not on your phone are probably kept in the app's local cache.
You can fix this by resetting the Phone Link app. This will delete all of its existing data and require it to sync with your phone again. On your PC, click to Settings, then programs, then Installed programs. Look for Phone Link and access its Advanced options. Click Terminate to close all the programs that are operating in the background. Then click Reset and confirm. After that, restart your computer and open Phone Link again. This will start a new sync and should get rid of those fake messages.
If the problem persists, you might have to totally unlink and relink your phone to force a thorough connection reset.
I hope this helps. If you have any questions, please leave a comment.
Thanks,