I just discovered this by happenstance moments ago, when I clicked on the spellcheck icon. A small window popped up claiming it would be run through Google's algorithm, and stored there. Very disappointed. So much for Sonic's advertising how they respect their customers' privacy! All the time I've been using spellcheck automatically, and never did this warning alert me. It's only when I turned off the automatic feature, and used the manual approach, did I learn of this intrusion on my privacy.
Our Sonic webmail page is completely Sonic made and operated, so there's no data going anywhere except for in house.
Spellcheck is done by your browser, like Google Chrome, Firefox, etc and stores any data inside your browser. It sounds like you are using Google Chrome and that's why your seeing the Google options when you are spellchecking words.
You can delete that data from within the Chrome's browser settings under, "Privacy & Security" if you ever feel the need to and it is a good idea to periodically clear data/cookies anyways.
I hope this helps!