Being poor means living a life of stress, financial and social.

Then why, during the experiment, did the poor participants and the rich participants have comparable scores when presented with a hypothetical easy financial challenge (a repair of $150)?

The claim the paper makes is that there are temporary challenges which lower cognitive functionality, that are easier to induce in the poor than the rich. If you expect that those challenges are more likely to occur to the poor than the rich (which seems reasonable to me), then this should explain some part of the effect- but isn't on all the time, or the experiment wouldn't have come out the way it did.

I wasn't meaning to put forward a study as settled science, of course; but I think it's interesting, and that they have a pile of other studies showing similar stuff. Now it's replication time.

While I have my doubts about the replicability of any social science article that made it into Science, the interpretation concerns here are assuming the effect the paper saw is entirely real and at the strength they reported.