I would strongly discourage use of Grammarly: It's essentially a keylogger which uploads everything you type to their cloud service, and there is really no guarantee of privacy or ability to delete that data.
I have the same concerns (and don’t use it for private writing) but I figured for public web copy it’s not a huge deal. Also, you can (or at least could) install their desktop app which would require you to do writing in it or copy/paste it in to get their suggestions. That way only the content you want to send to them goes, rather than everything.