How to hide a conversation
Once you have a conversation with someone, we don't show them to you around OkCupid anymore (because you've already liked and messaged them, so it's redundant to suggest them to you again). We keep them on the Messages page so you can find them if you want to, which is why there's no delete button - deleting them would hide them from you everywhere.
Of course, we realize sometimes you really don't want to see someone again, so to permanently remove a message from your Messages page, you can block or unmatch the person who sent it. That will remove the conversation from the Messages page for both of you, and prevent further messages between you, as well as hiding you from each other throughout OkCupid.
If you still need help, you can email firstname.lastname@example.org