There's no option to "delete" your side of a conversation. I understand that conversations are actually private threads, so perhaps deletion doesn't work (as it would affect the other side). What does "Leaving" a conversation do? That gets it out of my inbox, which cleans things up, but can the other person still reply? Are there any side effects? If not, and if "leaving" is the best way to get a conversation out of my inbox, Is it absolutely necessary to give me a second popup once I choose to leave the conversation to ask me whether or not I want to block the user? This is just an extra click, an extra spot to make a mistake... I think there's a bit of room for improvement here.
Conversations are deleted when all participants leave it. The extra click is again by design. That unfortunately cannot be changed.