Butterflies for the lazy gardener

Here's a dilemma. My weed clearing is going well. I've got the unwanted plants under control. The wanted plants are still running rampant, but one thing at a time, eh?

The last weed to get the chop is the most persistent — pellitory of the wall (Parietaria judaica). It's a tricky one. The stems are long and brittle, breaking easily and leaving the roots firmly in place. The leaves and seeds adhere to everything. To cap it off, the pollen causes allergies in some people. (An alternative name is asthma weed.)

So what's the dilemma?

It's a host plant for caterpillars of the Australian admiral (Vanessa itea). Do I eradicate pellitory in the garden? Or do I leave a patch for the caterpillars?