If you do not want your profile, photos and videos to be available to everyone on the Internet, you have to set your Instagram account to "Private" (check here how).
When you change your privacy settings on your Instagram app, the change occurs on all third-party apps pretty much instantly.
But, this won't be reflected straight away on Google's search results:
It takes a few days for removed content not to appear in results. What you see in Google's search results is what Google has "cached". (Google does not display real-time information, it takes Google a few days to crawl the entire web and the search engine uses what was there last time a page was visited).
Because cornbit is an authorized third-party service using Instagram API to provide an alternative way to browse Instagram.
When changing your Instagram account settings from Public to Private, this will be reflected instantly on cornbit but it will take some time to be reflected in Google's search results.
To remove your profile from CornBit, send a removal request in this url: http://cornbit.co/account-removal.php
Please note that removing your cornbit profile does not impact your Instagram account in anyway. As long as your Instagram account exists, people can view your photos using cornbit or any other web viewers.
However you can also set your Instagram account to "private'"(check here how). This will make sure that only your followers will be able to view your photos.
To delete your Instagram account, please go to Instagram support platform: https://help.instagram.com
To join cornbit, you need to have an Instagram account. There is no other way to sign up/in than entering your existing Instagram username & password. For more info on creating an Instagram account, look here.