Im not sure about mobile but if you're on a computer click the little white box next to the conversation and a small window will pop up. choose "leave conversation"
I need to go through mine since I've got 15 pages of them at the moment. On the side of each confab you'll see a box you can check. When you do a pop up will show up and you can "leave conversation" to delete them. If you've just made a response and want to get rid of it, then go to the top of the confab and you can do the same thing.