SumOfUs bills itself as "a global grassroots movement for corporate accountability." In an interview, SumOfUs Campaigner Martin Caldwell told me that Aldi's association with the greenhouses is practically a given, since "all the large European supermarkets source from Southern Spain."

"The Guardian article is written for a British audience, so that's why they mentioned British supermarkets," he said. "But all the European chains source from Southern Spain, and Tesco, Aldi, and Carrefour are the number one supermarkets in the UK, Germany, and France, respectively... [that makes them] the number one customers of [the greenhouse growers in] Southern Spain, if you like, so they have an acute responsibility to make sure that their suppliers are disposing of this plastic properly."

Caldwell said that SumOfUs was naming Trader Joe's in order to attract the interest of consumers in the U.S., and the fact that "its parent company Aldi is involved in sourcing this material" legitimizes the association.

But Aldi's connection to Trader Joe's isn't straightforward. As Rebecca Schuman recently explained at Slate, Aldi was split into two branches by brothers Karl and Theo Albrecht in 1960: Aldi Nord and Aldi Süd. The companies are completely independent from one another. Trader Joe's is a subsidiary of Aldi Nord, which also operates stores in Belgium, Denmark, France, Portugal, and Spain. The Aldi markets that are ubiquitous throughout Germany and the rest of Europe—and are also present in 32 states here in the U.S.—are owned by Aldi Süd.

In short, Trader Joe's doesn't have any connection to the giant chain that actually operates in Germany. And while it's possible that the grocer's corporate cousins elsewhere in Europe source from Spain's environmentally troublesome greenhouses (some of the stores are in Spain, after all), we don't know for sure.

"I hear what you're saying about Trader Joe's and Aldi," Caldwell said, after I suggested the link between the two might be somewhat weak. "For us, the connection is very strong. If the U.S., which is one of Aldi's biggest markets—if Trader Joe's was sending the message back to Aldi's headquarters in Germany saying, 'We're coming under a lot of pressure from our consumers to make sure that we as a whole group are doing something about this issue,' then they will respond very quickly."

419,000 people had signed the petition as of last Sunday, when Caldwell and I spoke, and it's soon to be the most popular petition on SumOfUs.org since the site's launch two years ago.

I asked Caldwell if there was any other way to put pressure on the greenhouse growers directly, instead of the grocers. "It would essentially be through governmental action," he said. "And with such an important industry like there is in Southern Spain, the government, particularly given their economic issues at the moment, they're unlikely to be intruding very heavily with extra regulation.