The correct option is C whether, or
Correlative conjunctions are pairs of conjunctions that work together. Some examples are either/or, neither/nor, and not only/but also. Correlative conjunctions are pairs of conjunctions that work together. Some examples are either/or, neither/nor, and not only/but also. We use whether … or to introduce a clause giving two options or alternatives. When the subject of the main clause is the same as the subject of the whether-clause(s), we can use whether to + infinitive or whether + a finite clause. In the given sentence the woman expresses a doubt whether they wanted to be invited or not. Thus whether must be used. Hence Option C is correct. Both' refers to the whole pair and is equivalent to "one and the other". The combination both/and indicates that the two items are equally presented and included. Hence Option B is incorrect. When using not only . . . but also in a sentence, parallelism should be the goal. It means that the words following both parts of this correlative conjunction (i.e., not only and but also) should belong to the same parts of speech. Thus Option D is incorrect.Either/or - are used together to offer a choice between two things but the given sentence expresses a doubt. Therefore "whether' is much more appropriate than 'either...or' and Option A is incorrect.