If you download Telegram from the website, it installs itself by putting a binary in ~/.TelegramDesktop.

If you install through this method, Software finds the app and shows it in the installed list, but it's empty of details and nothing happens when you press the remove button.

I spent quite a long time confused by my inability to remove the app! In the end it turns out that you just have to remove the hidden folder in your home directory (see http://askubuntu.com/questions/819521/how-to-remove-telegram).

The main issue here is that Software presents a remove button that doesn't work. I actually wonder whether we should display Telegram at all, if it has been installed in this manner (assuming we can't do anything useful with it, or show any useful information about it).