It doesn't look like you can actually delete them as such Sargey.
You do have the option of leaving a conversation. If you do that it will remove it from your list though I gather it technically remains upon the list of the other participant or participants who have been invited to join the conversation.
You are for the record given the further option when you leave of whether you want to be alerted if or when somebody else makes a new reply to choose whether you wish to return or not. But in the end the way it works presently you cannot delete a conversation in the absolute sense.