Senator Bail Organa tells an underling to "wipe the protocol droid's memory" near the end of Revenge of the Sith.
Did anybody copy those memories into storage before the mind wipe?
Given C-3PO's history, that would be tempting. The royal family of Alderaan would get some inside information on the Jedis and the politics of Naboo from looking through all that C-3PO has seen and heard.
Is there any indication from the extended universe that anybody made a backup copy of C-3PO's old memories?
"I'm placing these droids in your care. Treat them well. Clean them up. Have the protocol droid's mind wiped." ―Bail Organa
This is the event of which you speak. It occurred in Episode 3 shortly after the birth of Luke and Leia. None of the mentions of this event in Canon (or Legends that I know of) refer to it as anything other than a wipe.
C-3PO's memory was erased, though R2-D2's memory was not.
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Due to Threepio's talkative nature, Senator Organa made arrangements for the protocol droid to receive a memory wipe.
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Due to his general inability to keep secrets, Bail Organa arranged for him to receive a memory wipe in order to preserve the secret of Anakin and Padmé's offspring, Luke and Leia.
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Shortly after the Galactic Empire was formed, Bail Organa had C-3PO's memory wiped clean in order for the droid to not spill any confidential information.
(from C-3PO & Memory Wipe | Wookieepedia)
Given the importance of hiding the Skywalkers, it seems that Organa would not have a backup lying around. Since the Jedi were now defunct, there was no reason to try and scrap C-3PO's memory for information. And as a fellow Senator and close friend of Amidala, it is likely that Organa already knew everything that she did. Remember that Amidala had not been Queen for almost several years at that point, and she didn't get C-3PO until after the events of Episode 2. So he had no memory of that in the first place. Once she became a Senator, she would have been less involved in the domestic politics of Naboo (which has questionable importance to anyone off planet).
So given the complete lack of evidence of a backup being created, and the high importance of keeping the twins a secret, I would say that no copies were created and that the memory wipe was complete.
But what about R2-D2? Why did he keep his memories if the secret was so important? Because R2-D2 didn't have a habit of saying whatever came into his circuits. I'll leave it at that since it is addressed in a different question/answer.
