Pappas' links to the Greek article of her announcement where she goes into more details about the citizenship (it was originally in Greek so pardon the poor online translation). It looks like she was officially granted Greek citizenship back in December 2015 and was sworn in in January 2016.
http://sportsfeed.gr/2016/02/26/me-tin-ellada-stous-olympiakous/
"It was in February 2014 when through an unexpected coincidence I discovered that I could to make my dream come true and to fight for Greece at the Rio Olympics. It was then that I met in Eugene, Oregon with the head contact and the type of world John federation Nicholas, who showed me the way and was for me a valuable advisor.
Today, in February 2016, just two years later, my dream starts implemented, since I'm typically a proud Greek national. On December 22, 2015 was informed officially by the Greek authorities that they now have the Greek citizenship and January 8, 2016 sworn 'to guard loyalty to the Fatherland, obedience to the Constitution and the Laws and conscientiously perform my duties as a Greek citizen. "
It is something I could have done for years, but I lacked the knowledge and proper motivation. This gained the possible participation in the national team and represent Greece in international competitions. The thrill of my father on hearing of young people was unprecedented. Even greater was that of my grandmother Mary Rhodes, which put tears upon hearing the news. It is something that I felt the need to do all my relatives in Greece. "
Also, Pappas was considered a Greek/American dual citizen through her father and paternal grandparents. Her paternal grandparents were Greek nationals who emigrated to the USA in the 1950s.
According to the Greek nationality law: "An ethnic Greek born outside of Greece may acquire Greek citizenship by naturalization if they fail to qualify for simple registration as the child of a Greek citizen. (This provision excludes Greek Cypriots, who may seek Cypriot citizenship instead.) The applicant must prove that at least one parent or grandparent was born a Greek national."
https://en.wikipedia.org/wiki/Greek_nationality_law
As for her sponsors... this is what she has listed on facebook:
"Thank you to Café Mam, Runa, Wild Friends Nut Butter, Newman's Fish Company & Newman's Fish Grotto, Long's Meat Market, EnduroPacks, Great Harvest Bread Co. Eugene, OR, Beet Boost, The OG Corner Market, Mammoth Lakes Crib, and Track Town USA for the incredible support-- 2015 was fun but 2016 will be even more incredible."
https://www.facebook.com/media/set/?set=a.1705835922973255.1073741834.1573401692883346&type=3