I’m familiar with this issue. The basic reason is that the APT repository version of Telegram is older than the one used by the majority by several versions.
This is easily resolved via the SNAP version of Telegram. However, you’ll need to enable snap installs on Linux Mint. This can be done by opening a terminal and typing:
sudo rm /etc/apt/preferences.d/nosnap.pref
Then the process is simple:
sudo apt update
sudo apt install snapd
For snapd to function you will either need to reboot your machine or log out and then log back in. I’d recommend the former, just to be 100% certain.
Once you reboot and login, purge the currently installed Telegram, if you have it installed by typing in terminal:
sudo apt purge telegram-desktop
Once that one is done, go ahead and type:
sudo snap install telegram-desktop
This will take a bit longer as SNAPs create a self-contained version of an application with all its dependencies and libraries in one place. Most of them also function in sandbox mode which means they run in an isolated part of the system’s memory.
Once done, run Telegram and please let us know if your issue was resolved. 