Rated 3 out of 5 stars

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.

This review is for a previous version of the add-on (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.