Their habitat plant is the NZ Swan Plant (Ascelpias physocarpa), which is also the habitat plant for the New Zealand Monarch caterpillar.
The caterpillars are long, narrow and green and have four tiny black spots on each side of the body behind the head. It can be difficult to see them because they are the same green as the swan plant leaves.
The caterpillar weaves a sticky web around the swan plant leaves and flowers which soon dry out and die. You can tell that the infestation is swan plant moth caterpillar because of the tiny little black 'seeds' of their poo everywhere.