The correct answer is: A. some.
The word “some” is used to refer to an indefinite number or amount of something. In this case, it is used to suggest that the woman is more clever than we are aware of.
The word “many” is used to refer to a large number of something. In this case, it would be too strong to say that the woman is more clever than many people know, because we do not know how many people know how clever she is.
The word “a lot” is used to refer to a large amount of something. In this case, it would also be too strong to say that the woman is more clever than a lot of people know, because we do not know how many people know how clever she is.
The word “none” is used to refer to no amount or number of something. In this case, it would be too weak to say that the woman is not more clever than we know, because we do know that she is more clever than we know.