Integrating Grammarly with online LaTeX editors such as overleaf?

I used to copy and paste, as Hamid suggested until recently. I created a chrome extension that copies the .tex content; filters the commands/keywords and pastes the plain text in a textarea. This textarea is displayed over the pdf preview and all textareas are scanned by Grammarly.

It is not yet on the store, but you are able to install it if you are only a bit technical. You can find it here: https://github.com/robindijkhof/overleaf-textarea

EDIT: I created a new version. Changed made by Grammarly are automatically merged back to Overleaf. I published it to the Chrome store, it is currently waiting for a review.

EDIT: It is now available from the store. https://chrome.google.com/webstore/detail/overleaf-textarea/iejmieihafhhmjpoblelhbpdgchbckil

EDIT: JFYI, it's also available for Firefox: https://addons.mozilla.org/en-US/firefox/addon/overleaf-textarea

In overleaf, if you select rich text mode, then Grammarly works when you write a comment. This screenshot shows the idea:

Update: to somehow make it faster to check, you may select the text you want to analyze and press the comment button so that the text goes directly in the comment and Grammarly checks it instantly.

As a suggestion, I usually write the whole article then check all of its content (all latex document) by Grammarly desktop and also languagetool (and also maybe some others) together to proofread it completely. Then, I refresh the file by copy and pasting the result into the editor (in my case texstudio but you may copy and paste in sharelatex).