#datesandfigs

It’s so hard to tell - logically, they shouldn’t remember much, at least whenever it related to the Silence. Canton, having not been reminded about the Silence for a while, seemed to not remember a lot of it after only three months:

CANTON: Why didn’t you tell me this before we started? DOCTOR: I did, but even information about these creatures erases itself over time. I couldn’t refresh it because I couldn’t talk to you.

And Rory:

AMY: That’s what we’ve spent the last three months trying to find out. RORY: Not easy, if you can’t remember anything you discover.

So, unless they refresh the information, those three months probably seem awfully muddled (on the other hand, they should still retain some information about what they did, but who knows how much sense that makes once the information about the Silence gets deleted).

However:

they retain the system of tally marks (the Doctor marks his arm in The Wedding of River Song)

it is unknown how much information got through to Amy, even with time stopping - did she find out everything herself or was some of it from before?

Amy remembers killing Kovarian in spite of all the Silence running around at the time, so important events apparently don’t get deleted alongside, at least not immediately

River seems to have the best chance of remembering the Silence, after all, she managed to shoot one when it was standing behind her. She remembers her conditioning, the basic points of her early life: “I was trained and conditioned for one purpose. I was born to kill the Doctor.”

But in Closing Time it becomes clear that she is missing all important details:

RIVER: You know about the Doctor? KOVARIAN: So very well. Oh, don’t try and remember me. We’ve been far too thorough with your dear little head. RIVER: Oh! What are they? What are those things? [referring to the Silence] KOVARIAN: Your owners. RIVER: My what?