How to Extract XBLA Title Update onto USB Stick?

Hello, I hope I am in the right forum, because I’m new here.

I have an Xbox Live Arcade game on my 360 and I want to copy a title update from my Xbox 360 to a USB stick. I already have properly formatted it and managed to get the core game, but I cannot get the updates which I have installed for it. How do I copy these?

Searching around, I’ve found plenty of tutorials for how to install title updates to an Xbox 360 via a USB stick, but none the other way around. How do I copy those TU files from my Xbox 360’s Hard Drive to my storage device? I can see the game in Horizon under the Games tab of the Device Explorer, along with its DLC, but Title Updates tab is empty.

Thanks in advance.

EDIT: I should also add that my Xbox 360 is not JTAG