It seems that there is still no ready integration between Notepad++ and Grammarly:
Grammarly cannot be used in Notepad++ because there is no support for it, like for example the add-on for MS Office products.
The only way is to copy/paste text between the Notepad++ software and Grammarly software, which is very time consuming.
community.notepad-plus-plus.org/post/51132
You can write your own plugin if you understand Grammarly API.