That document is a diet in preparation for RAI specifically designed to deplete the body of Iodine levels so that the I131 uptake is most effective, so should be treated with caution.
Even individuals with Hyperthyroid conditions need to have a normal iodine intake, yes they need to be wary of excessive iodine intake, but a normal intake should be fine.
The topic has raised some interesting questions, I have also not been able to locate any specific information on iodine content of fish oil, so to that end have sent an email to the supplier of the product my partner uses to pose this question.
She has used this particular fish oil, an ultra clean version to eliminate any risk of heavy metal contamination, for the entire period of her treatment and has not noticed any ill effects.
With regards to plant based Omega 3 this is Alpha Linoleic Acid (ALA) which is the Parent Omega 3, although most animals, particularly herbivores convert ALA well to eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), humans are not particularly good at converting it, even with a high intake of ALA at best we convert around 18% to EPA and only 5% to DHA, so it is very difficult to maintain adequate EPA & DHA levels.
Although we do use a certain amount of ALA in normal metabolic functions, we also need to consume EPA & particularly DHA through our diet.
