Here's what the National Organic Standards Board Policy and Procedures Manual says regarding genetically engineered foods:
"1.11 Genetic engineering (recombinant and technology) is a synthetic process designed to control nature at the molecular level, with the potential for unforeseen consequences. As such, it is not compatible with the principles of organic agriculture (either production or handling). Genetically engineered/modified organisms (geo/gmo’s) and products produced by or through the use of genetic engineering are prohibited."
"1.12 Although organic standards prohibit the use of certain materials such as synthetic fertilizers, pesticides, and genetically engineered organisms, they cannot ensure that organic products are completely free of residues due to background levels in the environment."
I take that to mean that foods which display the USDA Organic label are free from genetically engineered ingredients ... mostly. (Foods bearing the USDA Organic label are only required to contain at least 95% organic ingredients.)
I also take that to mean that if we don't implement practices to control non-deliberate contamination of organic crops by genetically engineered organisms, the claim "organic" will have little meaning.