Because you are running on a remote machine that potentially is accessible by others and being able to update to GitHub involves giving permissions, for security reasons it isn’t advised. See here.
As you start doing more, you may eventually want to look into running git with GitHub access on your local machine. You’ll still have the download step from the running session machine to your local machine, but after you bring the updated versions of notebooks and files to your local machine, you can be using git to push updates to your repository and take advantage if version control and powers that git offers.