The period when the great painted caves at Lascaux and Altamira were occupied by Upper Paleolithic people
has been established by carbon-14 dating, but what is much more difficult to determine are the reason for their decoration, the use to which primitive people put the caves, and the meaning of the magnificently depicted animals.
(A) has been established by carbon-14 dating, but what is much more difficult to determine
are -> "are" is incorrect, we need singular verb.
(B) has been established by carbon-14 dating, but what is much more difficult to determine is ->
It is better. Let's keep it.(C)
have been established by carbon-14 dating, but what is much more difficult to determine is -> "the period" subject is singular, so "have" is incorrect to use.
(D)
have been established by carbon-14 dating, but what is much more difficult to determine
are -> "the period" subject is singular, so "have" is incorrect to use.
(E)
are established by carbon-14 dating, but that which is much more difficult to determine is -> -> "the period" subject is singular, so "are" is incorrect to use.
So, I think B.