Ask Mr. Smarty Plants

We are at something of a disadvantage in trying to answer your question. The Lady Bird Johnson Wildflower Center (home of Mr. Smarty Plants) is committed to recommending the growth, propagation and protection of plants native to North America. Dietes bicolor (African iris) is native to, well, South Africa, and therefore  to neither North America nor Australia. It is widely grown in Central Texas, though of course not at the Wildflower Center. Since we have no experience with it, we were not aware of any tendency to invasiveness. The main problem in getting rid of it is that its root are rhizomes.

Rhizomes are horizontal underground stems that strike new roots out of their nodes, down into the soil, and that shoot new stems out of their nodes, up to the surface. This rhizome activity represents a form of plant reproduction. The irrepressible nature of much of the vegetation you'll find on invasive plants lists is due to the vigor of the rhizomes of these aggressive plants.

Looking at these images of rhizomes will help you understand how difficult your task may be. If the plants you have in your garden are not too large, you may be able to dig out the whole network of roots in one mighty shovelful, but probably not.  After removing as much as possible, and discarding the clump of dirt with the rhizomes in it where they roots won't be able to reproduce yet again, try to kill any remaining portion of the rootlets left behind. Our practice in getting rid of plants that obnoxious is to obtain a small bottle of a wide spectrum herbicide that will kill just about anything, along with some small sponge disposable paintbrushes. If you find a small new plant coming up, cut it off as close to the soil as you can, and then paint the cut root end with some of the herbicide. You must do this quickly after cutting before the rhizome heals itself over to protect the rest of the plant. Properly administered, that herbicide should be able to destroy at least that little fragment of the plant. Prepare to repeat this many times before the rhizomes finally are defeated.