He should be able to recall recalling it though.
Which tells us that the memories of his soul can transfer to the memories in his brain. What Molly did was, apparently, wipe the memory right out of Harry's head, affecting his brain. It wouldn't have been a matter of just blocking the memory, like what Lea did to Susan in
Grave Peril, because Mab would have sensed something like that. It couldn't be an active spell. It had to be something that Molly did right then, which would permanently alter Harry's memory for good, or Mab would have been able to see signs of it. At least, that's how it seemed to me, especially when Harry and Molly were talking about it.
And if that's what Molly did, then there was no spell hanging around afterward for anyone counterspell. It would have been like brain damage, really; a very selective form of brain damage.
So, if we assume that's true, then the fact that Harry can remember it now means that the memories of his soul can overwrite or add to the memories in his brain. Which also means that, if Harry can figure out how to do it, he can use the permanent memory of his soul to protect the more malleable memory of his brain. If nothing else, he could come up with a sort of automated spell-system to check his brain and compare the memory there with the memory of his soul, and write over the brain-memories if there were any discrepancies. Sort of like an error-checking system with computer hard drives.
Though, of course, that might be more easily described than done, but it seems like something a wizard ought to be able to accomplish, given enough time and motivation.