Most mistletoe is a parasite, although there are a couple of varieties that aren't. Unlike some other parasitic plants, mistletoe (most of it) doesn't invade the growth wood significantly, but it does take moisture and nutrient from the host's sapwood circulation and can weaken what it grows on.

Most horticulturist advisors recommend removing it (the parasitic kinds) from "good trees" where it's found growing. The mistletoe itself is unlikely to kill a host tree, but may weaken it enough to make it more susceptible to other pests that can damage it; and it can directly reduce productivity of orchard trees.

It's apparently difficult to just remove mistletoe, since the remaining bits will grow back rapidly. Removal of the entire host branch, for all branches it grows on is a usual method.

There's a chemical treatment, but it will also kill the host tree unless it's applied while the host is fully dormant. (Mistletoe is an evergreen, so it's always growing and susceptible to the poison.) Obviously the chemical can't be used on mistletoe that grows on an evergreen host. And the chemical treatment is a "listed herbicide" that requires application be done only by a licensed "tree surgeon" in the US.

John