I'd say Archive or Leave and Archive as Jorick suggested. I agree users shouldn't be able to be [i]invited[/i] back to that convo by the other participants, but the user themselves should be able to request a re-invitation, I think, in case they closed the convo too early. 

Delete seems to do what it says. Even on the oldGuild, or any other forum, if I delete a PM, someone else can usually still see their copy. It's not like a post where delete is complete removal, PM deletion is similar to email. I would expect the same behavior here, where whatever I do on my end of the conversation should have [i]no[/i] effect on the other participants. 

It might be nice if there was a third option, Mute, which simply cut off notifications for the convo. There would be some conversations that I'd like to be part of that are updated constantly, leaving me with six or seven PMs in the span of a few minutes, which will (eventually) generate a lot of emails and annoy me if I keep seeing the new PM indicator at the top. Mute would allow me to stop the notifications but still be able to participate in the convo and see new messages, they just wouldn't annoy me.