It is always a good idea to clean house once in a while, and this includes any social networks you may use. There may be stale or out-of-date information or posts that you would like to remove and, in some cases, clean out the whole thing and start over.
In the Twitter world, more and more tools are becoming available to help you manage your Twitter feeds and clean out old posts or completely delete everything that the public can see. One tool is an iOS app called DLTTR that gives you several options in the paid version, $1.99, to delete tweets, retweets, or replies based on your preferences.
Screenshots that show the Delete Tweets button and the options available include:
For more details, have a look at the iTunes DELETE TWEETS: DLTTR description page.