For a long time leading up to the Grammarly Desktop App I had a simple Keyboard Maestro script with similar functionality to what MacSparky has touted. Hit a keystroke, open the Grammarly web app, find the “new document” image, and then paste the text. It was wonky at best trying to rely on KMs image finder and timing everything just right.
Fast forward to the release of the desktop app. At first, I couldn’t have been more thrilled when it launched, but I quickly learned that it is pretty invasive in the system, having it run constantly felt like having spyware on my machine 24x7. My compromise is only to use Grammarly when I need it and to quit the engine when not using it. I wrote a very simple KM script to accomplish just this and sharing for others who may be interested. In short, I hit my hyperkey+G to open the editor to review text and then I hit it again when I’m done to shut it down. Simulating “Space” at the end of the code prevents the dialogue box from popping up each time. Super easy 
