If you enable the "Disable Lookup" setting from the context menu the extension doesn't communicate with any servers at all— everything is processed with a Javascript/WebAssembly OCR engine bundled with the app— it just may be of a sightly lower quality.
That's exactly what pressing "Disable Lookup" does.
We started a fairly popular Emscripten/WebAssembly port of the Tesseract OCR engine specifically to advance the state of client-side javascript OCR engines: https://tesseract.projectnaptha.com
However, there's a limit to the kind of performance that you can get out of client side javascript OCR engines— with a shared server you can get better recognition on certain popular images.
Here's an online notebook for trying it: https://observablehq.com/@tmcw/tesseract-js-v2-alpha