If you'd like to close, delete, or remove an app chat, swipe left on the chat row and it will reveal the close function. The app requires that you select a reason why you are closing a chat. The other person will be informed of the reason.
Don't worry - you can always simply choose "Not my Type".
If you try to block someone who you have an open chat with, the app will first ask you to close the chat. Once the chat is closed, you can then block the user.
Website chats cannot be closed from the app at this time.