You can manage the tweets that are posted when you login to DirectCam via the 'Manage Login Tweets' button that appears in your DirectCam Settings.
Using this page you can also add custom tweets of your own. When you login to DirectCam a tweet will be randomly selected from the list of system tweets and personal tweets. If you don't want a particular tweet to be selected, make sure the 'Use' box next to the tweet in question is not ticked.