"That is the lady (which / that / who / whom) I told you about." Which is correct? [closed]

That is the lady [which / that / who / whom / (none of these)] I told you about.

I failed this test question when I used none of the options, saying: "That is the lady I told you about". Some constructive criticism would be most welcome.

This is clearly an instance of a well documented phenomenon: the kind of language test where you have to guess at the ideology of the person or committee who made the questions. And if you want to perform optimally, you only have a choice between pretending to share that ideology and getting the help of a lawyer and a linguist.

The sentence in question is a main clause followed by a defining (restrictive, integrated) relative clause. We can rule out which because it's so generally unused for people that we can take this for a legitimate rule. All of the others are correct, including the 'zero' relative pronoun.

• That is not used in non-defining (non-restrictive, supplementary) relative clauses nowadays, but that's not what we are dealing with. The rule saying that that cannot be used for persons is bogus, as actual usage and properly edited language advice books show.
• Who is also correct because it's referring to a person and nowadays it's perfectly acceptable to use who where once whom was required.
• Whom is in many respects the best choice in formal English. It is the object case of who, which is appropriate (though not required, see above) because in the relative clause it functions as an object. (Digression: So many people nowadays test this in the main clause that this is arguably a new, alternative, correct rule.)
• The zero relative pronoun can only be used for defining relative clauses, and only if it is not the subject in the relative clause. There is nothing wrong about using it for persons. So it can be used here as well, and in fact that's an excellent, idiomatic choice.

The problem is now that there is a bogus rule forbidding that and an obsolete rule forbidding who. If the question was actually to tick all that are correct, that makes three in four chances to get it 'wrong' by guessing incorrectly about the ideology of the person who ultimately decides what is considered correct for the test. Even if they are fair enough to accept all valid combinations as correct - if they didn't say so at the beginning, such a test is still unfair because it puts those who know about the problem under inappropriate (and potentially dangerous) psychological pressure.

All of this said, if the question was really to pick a correct choice from the list of non-zero relative pronouns, then you did get it wrong by ignoring the instructions. The assumption in this case would be that you weren't sure about any of those on the list being correct and were looking for a way out.