A phone picture is not a TV connection
Finding a title on TeaTV and sending video to a television are separate actions. The website does not expose a movie-casting button because it is not the application playing the video.
Use the application that supplies the film
Google’s Cast instructions describe supported apps and a compatible receiving device on the same Wi-Fi network. Check those conditions before treating a missing destination as a movie error.
When the button is grey
Confirm the app supports the receiver you are trying to use. A phone browser, an Android player and an iPhone app can expose different controls. Do not assume a button works simply because another screenshot contains the same icon.
Captions on the larger screen
Start a supported session and inspect its subtitle menu. Compare the track language and timing again after the picture moves to the TV; screen mirroring and native casting can behave differently.
A straightforward fallback
If the viewing service has a supported television application, open the same title there. Use the name, year and intended episode rather than expecting TeaTV favourites to transfer playback progress.