Extension doesn't recognize the user is logged in. Its Terms of Service are also ridiculous.

"By uploading or entering any User Content, you give Grammarly (and those it works with) a nonexclusive, worldwide, royalty-free and fully-paid, transferable and sublicensable, perpetual, and irrevocable license to copy, store and use your User Content (and, if you are an Authorized User, your Enterprise Subscriber’s User Content) in connection with the provision of the Software and the Services and to improve the algorithms underlying the Software and the Services."