How does one move the TODOIST icon onto Chrome mail site?
We offer two separate plugins. Todoist for Chrome https://todoist.com/chrome and Todoist for Gmail https://todoist.com/gmal
The first one will add an icon to the top-right corner of your browser, but not inside Gmail. The second will add Todoist only to Gmail, but not the browser.
If you're referring to the Gmail plugin, please make sure that you don't have a Gmail Labs extension called "Preview Pane" activated and that your browser accepts third-party cookies. Also, please note that the "TD Add" icon only shows up once you open a message in Gmail.