Suggest you update the "We Do Not Track our Visitors." part of your privacy policy to state that whilst you yourself don't track your users, you do allow Google

Suggest you update the "We Do Not Track our Visitors." part of your privacy policy to state that whilst you yourself don't track your users, you do allow Google to do so (google-analytics.com) Also, where you say "the only cookie we use is to keep track of the most recent inbox that you've visited" - This isn't true. You use Google Analytics, so there is a cookie in use there too.