Regards,
Inceptions
On a computer, click the Messages link on Seller Hub (upper right hand corner).
On the list of messages use the Check boxes (orange arrow) and the Delete button at the top of the list (green arrow).
You're not a seller, so you don't need to go to Seller Hub. Just go to your My eBay > My Messages.
When you follow the instructions shown in the screenshot from @mr_lincoln , the message(s) will move to your Trash folder and remain there until eBay permanently deletes them in six months. Until then, messages are retained in case they are needed for reference by you or eBay.
Messages reside on eBay servers, not on your computer. You simply have a view into them.
