To Check your Gmail inbox through InTouch, simply make sure that you have the Google integration setup (For information on integrating google, click here)
Then you can navigate to the left hand menu and click on the Messages tab, which will only appear once the integration has been setup
This will then load up the messages section of which your Gmail folder will be the first thing to open. Shown below is an example. From here you can view your inbox, sent messages as well as sending them out to your important contacts