Visit the installed extensions section on GNOME website and remove it from there.

Remove it by deleting the extension files from

~/.local/share/gnome-shell/extensions/xxxxxx directory.

By now you have realized that there is no way to know if an update is available for a GNOME Shell extension except for visiting the GNOME extension website.

Luckily for you, there is a GNOME Shell Extension that notifies you if there is an update available for an installed extension. You can get it from the link below:

pphttps:extensions.gnome.org/extension/1166/extension-update-notifier/|Extension Update Notifier]]