Move Twitter conversation to a private message and include a button in your response to send a private message.

Just like with review responses, negative or controversial topics on Social should be handled privately rather than on a public forum. Twitter allows responses to include a button that invites the Twitter user to send the business a private message.

When you reply to a Twitter post, you will have an option in the Social Lives Streams or Inbox for Social Community Management to add a “+ DM Reply link” in your response. When a DM Reply link is included, Twitter will show the link as a button that says “Send us a private message.”
Clicking on the “Send us a private message” button on Twitter will begin a private message between
you and the end-customer.