After you protect your Tweets, only you and your approved followers can read your updates or see your Tweets in Twitter Search.
If you at one time had public Tweets, those Tweets will no longer be public or appear in public Twitter Search results. However, unprotecting your Tweets will cause any previously protected Tweets to be made public.
Twitter does not have the ability to remove content on websites other than twitter.com.
What If my Tweets have never been public?
If your Tweets have never been public (in other words, you’ve always had your Tweets protected in your settings), your updates should never show up in Twitter search or other public search engines.
If they are showing up in search results, change your password immediately and revoke untrusted third-party applications. You can also submit a request with the following information:
When this started happening
Where you’ve seen your private updates posted (Twitter Search, Google, Bing, etc.)