I use Google Messages as my default messages but Phone Link links to Samsung Messages on my phone. I delete messages on the phone from Google Messages but they still appear on Samsung Messages and I still see the messages I deleted when I connect to Phone Link on my PC. I have to make Samsung Messages the default to delete the messages already deleted from Google Messages and then reselect Google Messages as the default. Samsung and Google do not speak to each other and Microsoft Phone Link links to Samsung Messages not Google Messages.
I don't bother connecting to the Messages app through Phone Link. I still need to pick up my phone anyway and select Screen Casting so I just use my phone, set Samsung Messages as default, delete the messages then reselect Google Messages as default so I just use my phone. Go back to Phone Link on PC and messages are gone.