Where does it say that they record your visit to other websites?
"Usage information. This is information about the Grammarly Site, Software, and/or Services you use and how you use them. We may also obtain data from our third-party partners and service providers to analyze how users use our Site, Software, and/or Services. For example, we will know how many users access a specific page on the Site and which links they clicked on. We use this aggregated information to better understand and optimize the Site."
This is so broadly defined that it covers everything.