Apples Ipad has no obvious way to delete direct messages in the Twitter app, so here is the way to do it.
You require both hands to do this.
Select the message you want to delete, this will turn the background blue and will open the conversation window.
With your right index finger hold the conversation window, with your left index finger swipe the message you want to delete at the chevron >
The delete button appears at the bottom right of the message
Press this and the message will be deleted