For others who might be interested, the scan passed without incident. My injured foot was all wrapped up in a boot, but I think that was just to keep it still. Both my legs went into the machine. I don't know how many Teslas it was, but my tattoos did not feel or look any different during or after the procedure. I asked the technician about it beforehand just in case, and she said the only time it's an issue is with old tattoos, prison tattoos, and tattoos people have done themselves at home.
I had the same thought about iron, but I think the difference in magnetism is probably related to the iron being in an organic form (in your blood) vs. inorganic (in some tattoo inks). That's complete conjecture though, I really have no idea.