If the Iraqi translators want to keep the apostrophe, that is perfectly acceptable. There is no need to copy the way the ATA did it. Many Americans don't have a clue about apostrophe usage (although one might think translators would have a clue)
In America one often finds the apostrophe omitted. That doesn't make it preferable.
Farmers Market / Farmers' Market
(not so obvious which is better)
Men Room / Mens Room / Men's Room
Ladies Auxiliary / Ladies' Auxiliary
(not so obvious)
Writers cramp / Writer's cramp / Writers' cramp
(definitely not the first, but one could argue for either of the other two)
Greg Lee's suggestion, distinguishing translators as owning vs simply constituting the Association, is useful. However, based on your comment that the Iraqi association is government run/sponsored, not owned/controlled by the translators themselves, that advice would mean that the Iraqi association should not have an apostrophe, but the American association probably should have one.
The question might fairly be asked whether the ITA is really an "association", or instead something more like a "registry".