The correct option is B False
In this sentence, "It was they who climbed Mount Everest." the clause "who climbed M.E." does not affect the structure of the main clause "It was they". It modifies the object 'they'.
It's a relative clause that modifies the pronoun 'they'.
So, we can put this clause aside on concentrate on the main clause.
In the main clause, 'they' is not the correct pronoun used here. As you can see, 'It was ____' is the main clause, where 'It' is the subject, 'was' is the verb and 'they' is in the place of the object. But, 'they' is not an object pronoun. (An object pronoun receives an action, or follows a linking verb 'was' to modify the subject 'it'.) It's a subject pronoun, it is the doer of an action.
The correct form should be: them
'Them' is an object pronoun, and should be placed instead.
Hence, the given statement that observes the above sentence: 'The usage of pronoun is correct in the following sentence'
is false. So, option B is correct and A is incorrect.