Thanks for letting me know that it's not just gmail that has the reappearing emails which has been happening since the beginning of Sept for me and for a friend also who also uses gmail.

Here I thought it was due to gmail pushing out another update, but it must be a problem with a mail server.

What I've been doing is after deleting a few emails, I go to my trash box and delete those emails from there. As soon as I do that they no longer show up in my inbox.