telegram is a social application
It will show social card based on the same data as facebook (ie open graph data).
If you want to set an image for Telegram, you should set the Open Graph image in the metadata manager
What to do if the social card does not work?
Update with WebPageBot
If the social card on telegram does not work, you can go to the WebpageBot and asks for a refresh with the command updatepreview
Check the Facebook graph
There is no explicit documentation, but it seems that they use the facebook graph.
You can check that the image/data is present with the facebook graph debug tool.