If you'd rather not use the app, you can also go to web.telegram.org for an entirely browser-based experience. To log in here, enter the phone number connected to your account, then enter the code that's sent to your phone. You'll be immediately logged into your Telegram account.
There only appear to be x86 and amd64 packages available from the direct soure. You may drop an email to telegram if they were willing to crosscompile to armv7hl. A armv7hl built might run if wayland-compliant.
You might check that on a x86 SfOS platform before, like the Jolla tablet.
Did anyone notice that the Telegram desktop client is now fully scalable? It also works in the latest QEMU image of the Librem 5 with a little bit of tweaking. I used QT_QPA_PLATFORM=xcb /usr/bin/telegram-desktop to start Telegram...
Delete the following files manually
* Remove the Telegram, Updater files that you manually downloaded. (It is in the location where you extracted the downloaded zip file).
* Remove the file /usr/share/application/telegramdesktop.desktop