How do you get out the mission on time tangled island?

To leave Time Tangled Island, click on the time device on the bottom left of the page, and select "lab". This will take you outside Pendulum's Lab on Main Street, and you can take the Poptropica blimp.

If you have the Haunted House card in your Store Items (free), you can leave Time Tangled Island or Astro Knights Island without returning to Main Street : select Use on the Haunted House, then immediately leave and you will reach the islands map.

(*leaving space on Astro Knights parks your spaceship on top of the castle)