Okay, don't use it then. They make no claims of enhanced privacy and frankly it's unreasonable to presume a service such as this would do all processing locally unless you're paying a premium for that ability. Or did I miss the "Great for confidential documents!" banner? For most peoples' use-cases, this is not a concern.
There is simply no good OCR engine available that can run inside a Chrome or Firefox extension. The best available is Tesseract.js. And while this engine is fantastic as a project, its recognition rate does not come close to what is available server side.