If a page is deleted or changed, it will take some time before it is recrawled and updated by search engines. In the meantime, the page can still show up in search results. For example, if you do a Google search for your name and “twitter,” some of your Tweets will show up on the results page. These Tweets could include some that you have recently deleted. Clicking them will take you to an error page, but the content is still visible on the search engine results page.
As mentioned above, Google, Yahoo, and Bing allow you to request the removal of individual URLs from their respective results pages.
If you want to avoid this happening altogether, you can use the protected Tweets option within Twitter. This should prevent search engine crawlers from indexing your Tweets, although any new followers will now have to request permission to view your posts.
To change your Tweets from public to protected, click the three-dot menu icon and go to Settings and privacy > Privacy and safety. Under Tweets, check the box next to Protect your Tweets.