Hello @Herve_Buisset,
Tricky one, I am on a Mac and not really able to troubleshoot on Windows. I would also assume that has to have something to do with the system spell-checker. I also rule out Asana.
You can try by deactivating the browser’s spell checkers, but honestly, I don’t see a connection with the app there. At least you can rule out that option by testing and go by exclusion.
You can try, if not done already, the holy IT solution, after deactivating the Windows spell-check, make sure you restart your machine and hope for the best… 
You can also have a look at this post where a user was having an issue with spell checking in the App as she was using the App in multiple languages. Maybe it sparks some ideas for testing, you can test the behaviour for instance on your browsers and see what happens there…