I don't know how easy their api is to work with (or if they even have one), but this would be a very welcome addition. Grammarly is a very powerful grammar checker.
It would be nice though to take a look at other tools which I have listed here. There English language linters and palgarism checkers which I have linked there as well.
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There's no API ( https://www.grammarly.com/answers/questions/913-api/ ) so we cannot do anything.
And even if there was, we already have LanguageTool, so support of another grammar checker is not a priority.
Last edit: Tim Hoffmann 2016-11-23
It would be nice though to take a look at other tools which I have listed here. There English language linters and palgarism checkers which I have linked there as well.