Google Tasks has some integration with Gmail. If you access your Gmail in a desktop browser you should see the option to open your Google Tasks on the right of the screen. This functionality allows you to drag an email from your Gmail inbox and add it as a task in your Google Tasks.
If you use this functionality or have used it in the past Taskary will ask you for permission to access your Gmail to download any Gmail messages associated with a Task
Taskary only downloads messages during sync from Gmail that you have explicity associated with a Task
If you use the Inbox Review screen, Taskary will load the contents of your Gmail inbox to allow you to create tasks from a Gmail message.
Taskary only stores Gmail data you explicitly assign to a Task
The rest of your inbox loaded in the Inbox Review is discarded once you close this screen.