The sad answer is that you can't access the source code of a webpage directly from the TWebBrowser. You can't access it because the TWebBrowser in FireMonkey is cross-platform and that means it must work on all platforms. Android and iOS does not support and allow this, which means the Windows Desktop version of TWebBrowser can't allow this either.
You will have to use a different component to do this, probably a third party component.
I am not sure if this will help you or not, but here is a link to something that might help: http://firemonkeylessons.blogspot.tw/2015/01/get-htmljson-from-twebbrowser.html