Your local movie list
My List, series checkpoints and the selected viewing country are stored in the browser you use. The catalog does not require you to submit a name or email address to save these preferences. The stored list is not an account shared automatically across devices.
Removing saved information
Open a saved title and use its saved button to remove it. A series checkpoint has a separate Clear checkpoint control. You can also remove this site's data through the browser's settings, but doing so removes the local preferences together. A home-screen shortcut does not prevent that removal.
Artwork and outside pages
Movie posters and backdrops load from TMDB's image service. Your browser contacts that service when it requests the images. Watch now opens JustWatch; choosing another viewing service there takes you to that service's own page and policies. Preferences and accounts held by those services are separate from My List here.
Shared devices
Anyone using the same browser profile may be able to see the saved titles and checkpoints. Use the removal controls when you no longer want a title kept on a shared device. Private browsing generally does not retain the same list after the private session ends.