Chain jumping off lower pulley

[Gunk]

This is what worn wheels look like. Even these weren’t really shifting badly. New ones are running smoother.

View attachment 532430

This is worn!

 

[Ajax Bay]

Get a spirit level and hold it down the centre of the chain when in largest sprocket. Should be perfectly vertical in that plane. There are of course tools to measure this and to apply correction. It does not look far off so, again, I'd be surprised if that was the cause of the "irregular noise". Why 'irregular' if the cage is out of vertical?
As for @Gunk 's 'that is not a knife', 1000s of kms (as in 15+ depends on nature of terrain and cleanliness regime) of use will turn the jockey wheels into ninjas, but that assumes they have kept turning (ie been maintained, once in a while). @Gunk 's imaged wheel has stopped turning and the rider has failed to notice the additional friction, a bit of noise and the cage 'kicking around'.

 

[Ming the Merciless]

This is worn!

View attachment 532476

You win with your new lightweight climbing jockey wheels.

 

[Mike_P]

Cage definitely bent

Is it worth trying to straighten it or will it simply bend again once under tension?

 

[Ajax Bay]

Bend it. The cage is under very little compression or lateral moment so will not just bend back.

 

[Mike_P]

Fixed and new cable fitted, all working okay and managed to do it without getting soaked