Q: Can you tell me what this aberrant foliage is?
It is growing on a fringe tree which is 10 years old and this is its first appearance. It looks like mistletoe to me but surely I must be wrong.
If it is mistletoe, how do I get rid of it without harming the tree?
A: Your identification is spot on: mistletoe.
Although we commonly see mistletoe in oak trees, it infests hundreds of woody plant species. It is a parasite, depending on the host plats sap for nutrients.
Mistletoe is spread by birds, which eat the white berries and excrete the seed wherever they roost on branches. Indeed, the word mistletoe is derived from Anglo-Saxon words for dung and twig.
Mistletoe rarely kills trees but it can weaken the limbs. Little can be done to remove mistletoe from large trees. Cutting it off of a limb only retards its growth for a while. It eventually grows back.
However, on smaller trees mistletoe can be controlled by spraying the clump with the chemical ethepon (click for sources). This is done in spring before the tree leafs out.
I’ll leave it up to you whether to remove the branch on which the mistletoe is growing or to find the chemical spray.
Read more here.