No, Grammarly is not nagware.
"Nagware" is a term for a type of software that is free to use for a limited period of time, during which the user is frequently reminded to pay for the software in order to continue using it.
We offer a free version of our product as well as paid offerings, including Grammarly Premium and Grammarly for Business. Paid product offerings provide additional types of writing feedback that are not included in the free version. There is no limit to the amount of time you can use the free version of Grammarly. If you use the free version of Grammarly, you may receive emails promoting Grammarly Premium or other paid offerings, but you can unsubscribe from these emails at any time.