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It is that spell check going to the cloud, scanned and sent back or is it an offline tool like the old thunderbird spellchecker? It is a bit scary the "online" part.

Cette critique concerne une version précédente du module (4.4.0). 

This is documented in the description at https://addons.thunderbird.net/en-US/thunderbird/addon/grammar-and-spell-checker/: by default, the cloud is used and there's a privacy policy which describes the details. You can also run the server locally.