Twitter today launched a new feature for the Private Messages section that makes it more organized by adding a new tab for people who do not follow them under the name of requests.
After the update (if the Receive messages from anyone through privacy settings setting is enabled) you will find a new section with the name of the requests and will be assigned to messages from people you do not know and you must approve the message to go to the inbox.
The anonymous author will not know that you read his letter or ignored it until you accept his request here. He will know that you interacted with him. Even the media in the message can not be viewed until you choose to accept, in order to avoid bad images and so on.
The new feature began to reach successively today for Twitter users on the web and across applications on Android and iOS.