I only mentioned EDTA because I saw it on Amazon, obviously the thiolated chelators (DMSA)are the better choice for mercury.
The originator of the meme of Iodine being a mercury chelator, as far as I can discern, is Dr. Sircus. In one of his articles, which is widely parroted, he references one very obscure and impossible to find book to support his innuendo that 'iodine chelates metals'. I have not been able to find this book.
I will search for "Ted Zava" to see what he says.
He says this: One more thought. There are Iodine transports in the salivary glands, directing Iodine to the "silver fillings" which are constantly leaching mercury vapor. This has potential to bind a significant amount of mercury that may be retained for a longer period (but possibly non-toxic)