[kaffee]

Where does it say that they record your visit to other websites?

[vladletter]

And the cookies: "Grammarly uses cookies and similar technologies, including tracking pixels and web beacons, to collect usage and analytic data that helps us provide our Site, Software, and/or Services to you, as well as to help deliver ads for relevant Grammarly products and services to you when you visit certain pages on the Site and then visit certain third-party sites." Let's define those certain sites ;)

[exitnode]

Probably this here is meant:

"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."

[vntok]

Nothing out of the ordinary here. Virtually every website does this.

[spiderfarmer]

"We may also obtain data from our third-party partners and service providers to analyze how users use our Site, Software, and/or Services."

This is so broadly defined that it covers everything.

[gtirloni]

Yes, everything that Grammarly provides, not everything you use on your devices.