What hook can alter fully rendered html? I'm rendering some JSON using Views and Views Datasource and due to a bug in Views Datasource, I can't seem to get the output rendered properly. So, I'm looking for a workaround. 

What hook can I implement in my theme or module that will give me the final string that is about to sent back to the browser that will give me one last chance to alter it?

EDIT: I was in a hurry and worded that poorly. When I say the page won't render properly, I mean that the bug in Views Datasource doesn't use the proper data formatters for the data fields. I'm getting JSON back just fine, but some of the values within the JSON are not properly processed by the relevant module formatters. In this example, the Video field can contain a Video URL and a Thumbnail Image URL. The view is configured to display a Thumbnail Image URL, but due to the bug in Views Datasource, it is displaying the Video URL instead.

I can't just change the render array, because Views Datasource is not generating its output using a render array.
I highly recommend you not to alter the page output when you clearly know where the bug is. See Bala's answer. Or may be you want to let us know what is the exact problem ?

To answer your question, to alter the content that is going to be rendered, use hook_page_alter