I don't get why this question gets asked so often. Really, I don't. Is it that hard...? Nothing personal by the way, it's just something I've noticed. But, to answer your question: Jon (and the ones that were with him) and Sansa both speak the same language. I think it's safe to someone told her back at camp.
At the Battle Meeting, Sansa said to Ramsey, You willdie tomorrow ord Bolton... sleep well. Then she rode off. She did not hear the conversatoin about the dogs, ramsey said it after she left.
So clearly, Jon told her, after the beating, and he was taken away..that was when she asked where Ramsey was. We didnt see the conversation, but Ramsey was already tied up in the Kennels, so there is no other way Sansa could have known he was there, unless someone told her. IF she knew he was at the Kennels she wouldn't have had to ask.
It's an error. And it isn't nitpicky...it is very noticeable if you watch it more than once. And, hello, Sansa rides away from the war council before Ramsay talks about his dogs. It's an error that should have been resolved in the sequence.
Its entirely conceivable that Jon and the crew talked about it back at camp. Its not too much of a stretch. Think of it like the time after Sansa met up with Jon at Castle Black and they were talking about how Sansa treated Jon when they were growing up. Technically - we never saw Jon and Sansa together on screen - so then using the same logic question...then perhaps Jon never saw Sansa when they were growing up together because we never saw them together on screen - in any episode. Its completely logical to think that they had some interaction while growing up, even though we didn't actually see it.
Your question is one of a very very small detail - one that can be explained by hearsay. Maybe she should have said "Jon said you said you starved your dogs for seven days" or "Jon told me you said....", but that makes an awkward line. Much more powerful to say "you said it yourself...." which is true, he (Ramsey) did say it himself.
Its not a stupid or nitpicky question. It was definitely an error in production. It was originaly suppose to be Jon who fed Ramsy to his own dogs and spoke the line of the dogs starving. Sansa was suppose to look on and smile. For some reason production felt that giving Sansa the role of Executioner would be more impactful, and I think they were right. They just didn't pay attention to some minor details like this one. There is another error in detail in this episode with Sansa, and it is also because they chose to give her the executioner line instead of Jon. This is what happens when they change things in a hurry.
The thing is, there's not really much time for idle chit-chat, like who fed what dogs when... The sequence goes:
1) Sansa rides away from the parlay
2) Bolton says the "7 days" thing to Jon
3) Battle of the Bastards
4) The capture and imprisonment of Ramsay.
Now, I can no longer recall if Sansa and Jon have their "the battle was lost until you came with the Knights of the Vale ('who have also been known to say "Ni..." on occasion') conversation before or after she oversees the death of Ramsay. If this conversation happens AFTER Ramsay's death, then it's likely the first conversation between the siblings since Sansa rode of at #1 above. If it happens BEFORE Ramsay's death, then it's believable that the "7 days" nugget might have been shared between the Stark siblings. Well, between Jon Targaryen and Sansa Stark.
It’s not the 1st conversation. The parties to The Battle of the Bastards parlay, & Sansa tells Ramsey he will die tomorrow (at that time only she knew the Knights of the Vale were on the way.) Sansa retreats back to Stark camp. Ramsey tells them he hasn’t fed his dogs in 7 days. Next we see Jon & Co back at camp in war council in Jon’s tent talking about battle strategy. Davos & Tormund leave & Sansa asks Jon if it ever occurred to him that she would know more about Ramsey than anyone there? She doesn’t tell Jon about Littlefinger & the Vale, he doesn’t mention starving dogs. I think at this point Jon is still trying to protect Sansa, which she notes as her last line before leaving him is, “No one can protect me. No one can protect anyone.” (I love to note the use of the term “No one” whenever I hear or read it. I think the choice of wording is important. She doesn’t say “you [Jon] can’t protect me” or “we can’t be protected.” Or anything else. Sansa says NO ONE. But that is another matter.
I think there are 2 explanations for the Sansa knowing the dogs haven’t been fed in 7 days. Either it is a production mistake, OR, it is a subtle reference to Sansa indeed being a warg. We never got to see or read about Sansa having wolf dreams or learn about her connection to Lady because of Lady’s untimely death. But, I believe all the Stark children were wargs. And it may be that Ramsey was also a warg, bonded to his hounds.
Book readers get additional insight into warging & skin changing in ASOS & ADwD prologue POV of Varamyr Sixskins. Thru Varamyr we learn once a beast has been joined to a man, any skinchanger can slip inside it. Varamyr felt a weak Orell living in the eagle & overtook the bird, but he explains to Jon that warging works both ways & now Orell is a part of Varamyr thru the eagle.
We get more insight, thou very subtle, from Sansa herself when she speaks with Sandor during the S8E4 post Battle of Winterfell celebration... Sandor asks how she killed Ramsey and she says with hounds. As a book reader, I see that conversation as 2 wargs speaking because I believe Sandor is also a warg & that we best see that in ASOS Arya chapters when she describes Sandor’s relationship with his horse, Stranger.
Taking all these puzzle pieces & subtle clues, I like to believe that the scene between Sansa, Ramsey & the hounds is similar to the parts of the story I mentioned above. Ramsey is cocky confident his hounds won’t turn on him- I believe it’s cuz he’s bonded to them. But Sansa knows the hounds are starving because she senses it as 1 warg senses another, (Varamyr sensing Jon & Bran.) Sansa overtakes a hound & Ramsey, causing them to turn on their master. And just as Orell lived on inside Varamyr, Ramsey lives on inside Sansa... it explains the cunning & even ruthlessness we see in Sansa moving forward from this point.
...my 2 cents anyways. Finding clues we r not even sure are clues to tie puzzle pieces together to explain the otherwise unexplainable is why we all love this story, is it not?
That's some awesome insight! While I wouldn't put such intricacies beyond an author like Frank Herbert (who's utterly fucking insane, but unspeakably brilliant as a result), I'm sad to say I think this goes beyond the scope of what Martin is capable of. While I'm happy to be proven wrong, I currently remain unconvinced that Martin is capable of interweaving this level of detail into his stories (I've only read the 1st book in the series, so I guess it's possible he's become a better writer in the intervening years, though once again, I'm not convinced he's improved by the margin required to do what you've suggested).