Are they worms or a caterpillar maybe?

Every spring we get loads of caterpillars coming downing down from the oak trees and some will do damage to my brand new plumie leaves. This year on even ate the entire center out of a new tip on my poor 4-tip Leona Hoke. By the time I found it it was too late to do anything but curse :(

They don't usually do too much damage. A couple of years ago some very large caterpillars even ate big chunks out of the trunks or branches of various plumies, including one that ate a hole right to the center of the trunk of Makaha Sunn (!!), but all the plants just grew beautifully and you can barely tell on most now that there was any damage done.

If the damage looks really severe, try spraying with Spinosad a few times and that will kill the chewing or sucking insects that are the problem.