If Clara went back in time to save all the Doctor's past incarnations through Trenzalore's TARDIS, why doesn't Matt Smith's Doctor recognise her when they first meet from all of their past encounters across time and space?
From "The Name of The Doctor", in the montage that shows Clara saving several past Doctors:
CLARA [Narration]: I just know I'm running. Sometimes it's like I've lived a thousand lives in a thousand places. I'm born, I live, I die. And always, there's the Doctor. Always I'm running to save the Doctor again and again and again. Oi! And he hardly ever hears me. But I've always been there.
As I understood, Clara always saved the Doctor in his/her past incarnations, but kind of in a "behind the scenes" way. He hardly ever heard her, or saw her. In said montage, Clara was retconned with not very well done effects in past instances when The Doctor was in mortal danger, making it look like she saved him all along, without the Doctor knowing.
We see the first time he turns to see her is in "The Snowmen", and the Eleventh Doctor didn't even make the connection until he saw her grave saying Clara Oswin Oswald.
Oswin Oswald was the girl in the Dalek Asylum, and the Doctor never even saw her, he just heard her voice. That's when he finally put 2 and 2 together and set to solve the mistery of the "Impossible Girl", putting the time loop into motion.
The usual reason that the current Doctor doesn't remember some events that have happened to past Doctors is to do with time streams. This is the excuse used when a current Doctor event directly interferes with a past Doctor event. For example, the Doctor doesn't remember
he saved Gallifrey rather than destroy it
until the events responsible for that were present in his time stream. From the TV episode The Day of the Doctor
WARRIOR: I won't remember this, will I?
DOCTOR: The time streams are out of sync. You can't retain it, no.
WARRIOR: So I won't remember that I tried to save Gallifrey rather than burn it. I'll have to live with that. But for now, for this moment, I am the Doctor again. Thank you.
Only the Doctor performing actions responsible for altering their own past can retain memories of those events.
The events that lead up to Clara going back to save his past incarnations, and consequently the Doctor recognising her and being aware of her presence in his life, begin with Asylum of the Daleks or there abouts (he realises who she is in The Snowmen). As such, even though he had met her previously (it's shown that he met her face to face while
stealing borrowing the TARDIS, an event he remembers fondly and very well and would certainly remember the girl who helped him, as well as 10 and the War Doctor meeting her), he doesn't remember her because she isn't in the time stream of events that leads to her entering his past until 11's tenure as the Doctor. Essentially, he can only retain a permanent memory of her once the events that led to her spreading to his past had begun.
Presumably, the Doctor now does remember all of the times Clara had saved him/her in the past and that he/she met her, as the time streams have lined up now. Until that point when the time streams synched up though, any memory of her couldn't be retained.
The disconnect is between "she went back in time to save the Doctor" and "the Doctor had past encounters with her". The second does not actually follow from the first: she could have saved him without him ever seeing her, at least not to remember. A close analogy from real life would be EMT's/emergency room doctors: most people whose lives they save wouldn't give them a second look if they met in the grocery store.
The Doctor is able to change the past, even his own past (the events of Day of The Doctor, for example). When he changes history, events change around him - he retains the memories of what previously happened and what he changed. Even other versions of himself on those few occasions where he has met himself do not take the memories of changed events with them.
Clara may have gone into the Doctor's past and changed or influenced past events in his timeline, but as her entering his timeline was a direct result of Eleven meeting her and taking her to Trenzalore these changed events would have altered "around" Eleven so he would not "remember" the things that she changed as if they had happened to him.