Neither, doctor who gets involved somehow and the whole situation goes to hell, before resolving itself in some strange,ridiculous, and often Contray to the laws of physics way.

His name is not "Doctor Who". He is simply... The Doctor. And time travel does not break the laws of physics.
The angel would forget. Why would it be immune to the silence?

Because it's quantum-locked. There's no life in the stone to observe or be influenced by the Silent while the Angel is being observed.

Weeping Angels are living things. The are quantum locked, yes, but they are not inanimate objects.

If a living thing was locked down by the quantum Zeno effect, it would become functionally indistinguishable from an inanimate object. The system being frozen by observation is the entirety of the Angel's being, neurological impulses if it has any, muscle contractions and expansions, the flow of bodily fluids or whatever the Angel equivalent is.

I'm assuming the question only refers to a single Silent and the writer just didn't know that the Silence is their name as a plurality/religious order.

So youre saying that if the silence looked at an angel, said angel would become an inanimate object. And because an inanimate object has no memories the angel would not forget the silence? Interesting idea. However I dont believe they ever say if an angel can see or not when something watches it. (Seeing equates to brain activity) This might be an unanswerable question.

If an Angel can see while it is quantum-locked, quantum-locking is an even worse description of what happens than it already is. This remains a possibility because LOLSCIENCE and timey-wimey.

An angel can see when its quantum locked. I just thought of a way to prove it. I remember an episode, sorry I cant remember what one, where the Doctor tricked 4 angels to look at each other. When they saw each other they became quantum locked. If they cannot see when their locked they would have been able to move.
So if they can see when locked doesnt that mean a silence would be able to erase their memory?
Or, in that episode, would the angels just flash between being locked or not? Because that would see themselves one second and be locked the next.
Sorry if Im doing a terrible job explaining what I mean.

His name is not "Doctor Who". He is simply... The Doctor. And time travel does not break the laws of physics.
The angel would forget. Why would it be immune to the silence?

Meh, it doesn't matter that much, and I never said time travel breaks the laws of physics that foment was about how often some physicallyimpossible event such as a planet being towed through space or another planet suddenly Ppearing next to another planet and their orbitsdon go Fubar.