Millenco Lockmaster Mantis 3 lock - extra part after rebuilding

tl;dr – where does the horseshoe-shaped bit at the bottom of the picture go?

Long version

I’ve been trying to refurbish the locking mechanism (gearbox?) for my street door after it got so stiff the key broke in the lock.

I’ve removed the 5 point locking strip from the door and taken the gearbox off of the strip, and I managed to get the broken key out with pliers. I’ve now dismantled the gearbox in the hope I could just add some grease and put it all back together again, but it kind of fell apart when I took the screws out and I’ve been trying to do the resulting jigsaw puzzle for a couple of hours.

I’m pretty sure got most of the parts back in the right place, but there’s inevitably a small part left over that I’ve got no idea what to do with :-(. I’m hoping someone can point me in the right direction…

See the image below for the current state of the lock – I think it’s a Millenco Lockmaster Mantis 3 – see https://www.amazon.co.uk/Millenco-Lockmaster-Backset-Spindle-Mantis/dp/B01B516QYG.

The piece I can’t find a home for is the horseshoe-shaped part at the bottom of the picture. I think it goes at the bottom end of the lock somewhere, but that’s not definite…

Any help appreciated with either working out where it goes, or finding a teardown guide / reference image for the lock as I’ve had no luck finding either of those myself.