Is the iodine a potassium iodide? Not sure how much potassium is really there, it's just the other half of the salt (and I'm not sure what other iodine options there are--well, I take that back--there at OTC kelp supplements). I took high doses of iodine (Iodoral, then kelp) for thyroid problems while nursing--iodine (and selenium, if you care) transfer through to breastmilk at higher rates than most minerals (most top out at a certain point, they seem to limit). But I figured I was low, so baby was low too (I also took selenium, used the same rationale).
I've read iodine can mobilize mercury (from amalgam fillings, for example) and that wouldn't be good while nursing, but a) I didn't know at the time, and b) I didn't realize what other options I may have had, but I knew I was barely functional. Not sure if it caused any problems for baby or not. I'm taking adrenal supps (different kind, but I think the same idea) while nursing, and my HCP told me directly it was fine, and I'm supposed to have that stuff in my body anyway, this is meant to replace what I'm not making on my own.
No real advice on the iodine, you need to make your own call. Sorry.