Selling is the real part, no? I find no irony or double meaning there.
I think that the quotation marks are inappropriate—not so much because they fail to satisfy the rather mushy standards that determine when journalists may use so-called scare quotes (although they seem to fall short of any reasonable standard on that count), but because the whole headline is extracted from a single sentence of an actual quotation in the story. Here, again, is the headline:
And here is the in-story quotation that it is based on:
Clearly, the headline could have been "Women ... sold ... resold ... in ... name of tradition" with an attribution to "Snehlata Upadhyay" or to "Woman commission member," thus:
Or far better, paraphrased:
Or better still, with the quotation marks excised altogether and the fragments of Upadhyay's comment placed in the headline without any embellishment:
As the OP says, there is nothing ironic or double-edged about the words "sold, resold" to justify putting quotation marks around them but not around the rest of the quotation-based headline. The quotation marks don't work as a straight quotation, either, because the actual wording of the sentence where they appear isn't "sold, resold"; it's "sold but resold."
I can't think of any theory of journalistic accuracy, irony, or good old-fashioned innuendo under which putting quotation marks around "sold, resold" in the cited headline makes sense or serves a legitimate purpose. Instead it comes across as misleading and pointless.
Yes it does use the ironic quotation marks correctly.. In the sentence, the "bad" part was that that a woman was sold for money. The irony is that that she was resold.