How do these sites know what framework I'm using and how do I hide it?

Builtwith can recognise CodeIgniter based on the directory structure (and index.html files in every dir) afaik.

If they can see the directory structure of your site and the index.html files in those directories, you've probably got bigger things to worry about than whether they can recognize what framework you're using.

Bonfire

Practical CodeIgniter 3
CodeIgniter Testing Guide