I think I read that a toxic plastic is used but can't find that article. Here is what the watchdogs at Care2 say about no iron:
Shop for clothes with less textile finishing
“Finishing” is the last step in the processing of many conventional, easy-care garments. Textiles are treated with chemicals to make garments that are miraculously: wrinkle resistant, stain resistant, fireproof, mothproof, anti-mildew, ant-bacterial, and anti-static. The little problem here is that the chemicals used for finishing include formaldehyde, caustic soda, sulfuric acid, bromines, urea resins, sulfonamides, halogens, and bromines. Not things you really want rubbing against your skin or wafting up through your nose. (Not to mention the toxic wastewater run off during production and washing of these items.) The “new smell” of clothes is usually from a sizing that is used to prevent wrinkling during shipping and display in the store—it is temporary and will be rinsed out after a few trips through the wash. The other finishings, however, are heat treated into the fabric and are much more permanent. Watch out for labels like “stain-resistant” and “no iron.”