Hi, every message logged in the chatter (message, email, log an internal note, system notification) below the every document is stored originally in the model "mail.message" only, not in the current document such as "res.partner" (Customer Window).
You can find it through Settings -> Techical -> Email -> Messages.

There is no direct way to delete or edit it through the current document. You must go to the above mentioned messages menu and delete it.

You can find the messages regarding the current window through the url:
http://55621-8-0-accd3b.runbot.odoo.com/web?db=55621-8-0-accd3b-all&debug=#id=7&view_type=form&model=res.partner&action=60
In the above mentioned url, note down the id and model.

In the messages menu search -> advanced search -> Related Document ID : 7 -> Apply and Related Document Model -> res.partner -> Apply will give the message regarding that document. You can edit or delete it.