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:
Women ‘sold, resold’ in name of tradition
And here is the in-story quotation that it is based on:
"This is the manifested form of the tradition naatra, wherein women are treated as commodities and are not only sold but resold several times in the name of tradition. She becomes the source of earning for her caretakers be it father or husband," member of woman commission, Snehlata Upadhyay who is also the in charge of Rajgarh district told TOI [Times of India].
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:
Woman commission member: "Women ... sold ... resold ... in ... name of tradition"
Or far better, paraphrased:
Woman Commission member says women are sold, resold in name of tradition
Or better still, with the quotation marks excised altogether and the fragments of Upadhyay's comment placed in the headline without any embellishment:
Women sold, resold in name of tradition
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.