No melaleuca leaves

Does "No melaleuca leaves" mean "There are no leaves of melaleuca"? It appears not referring to "There are no melaleuca left/survived the wild fire.
I am not sure. Because it sounds odd.

Context:
EVEN for rehab, this is no ordinary hospital. For a start, most of the staff are volunteers. One of them, Sharyn Brown, shows me around the wards – shady, quiet enclosures dotted with gum trees, in which the patients sit. Whiteboards record their progress and requirements. “No melaleuca leaves,” one sign reads. Brown tells me that the hospital employs a “leaf searcher”, who scours the local forests to find foliage for dinner time. “This one,” she explains, pointing to a patient, “came from a part of the state where melaleuca doesn’t grow, so it would make him sick.”

Source:
https://www.newscientist.com/article/mg24232340-500-koalas-burned-in-wildfires-can-be-now-saved-but-the-treatment-is-gross/