(Edit: I made the classic mistake of confusing iris with retina. Sorry. I assumed you're talking about iris recognition here.)
Not invasive at all. SRI's "Iris On-the-Move" product is a gateway that people walk through; a long-range infrared camera images their iris as they're passing through. As long as you catch a glimpse of the green light as you're walking, they can match your iris template. See "Iris on the Move: Acquisition of Images for Iris Recognition in Less Constrained Environments", Matey et al 2006.
(I'm trying to vaccinate you from this idea, not convince you. I obviously hate the idea of iris scanners at airports. My point is that unfortunately it can be done, and we should be careful.)
If you think about it, there's an argument to be made that face scanning is the most invasive because it can easily be done at a distance without your knowledge. The depths of your eyes may feel more personal, but facial recognition is insidious.
Another reason I'm nearly certain this was face recognition is that DHS already has a database of faces -- your passport photos -- and thus they have something to compare to. They don't have an iris or retina database for U.S. citizens.
There's "invasive" in terms of "ability to identify you, times ease of capture." Irises (and maybe faces) are very invasive by this metric.
Or there's "invasive" in terms of how much cooperation it requires to match you. I think that's what parent meant. A biopsy DNA sample or interrogation would be most invasive, followed by maybe something like a cheek swab, then palmprint, then willing fingerprint (ignoring latent fingerprints), then iris, then faces being the least invasive.
