This will delete the individual message.
To delete the entire conversation, you can click on the more (three dots) at the top and click on Leave conversation > Leave.
But, if you have a lot of DMs on your Twitter account, then deleting one by one is a time consuming and irritating task (since Twitter has no bulk delete option).
So, you can use the Twitter tools on the internet for this task.
In this post, we will see 2 simple tools which help us to do this task easily. You can pick a tool you prefer. Let’s get started.