Ivy on a tree
While the ivy on the tree will not kill it outright, at least not at the moment since it's only on the trunk, it's not particularly healthy for the plant. It competes with light, nutrients, and moisture that should be going to the tree. It also creates a moist environment on the tree's bark which may attract wood-destroying insects. If the ivy were permitted to keep growing, it would eventually cover all the branches, and probably kill the tree as it covered the tree's leaves.
Ivy can only grow from roots in soil (it cannot root itself to tree bark). To remove ivy growing on the tree, cut and remove all vines to a comfortable height around the trunk of the tree. This will kill the upper vines; the lower vines will need to be pried off the tree and pulled out of the ground.Try to minimize damage to tree bark. Mulch the area afterward.
Your ivy (Hedera helix 'Variegata') is not on the noxious weeds list in King County, although four other varieties of Ivy are listed.