Dear K Wilson

Thank you very much for your inquiry. I am no expert on trees, but I know a few. So, I went to Susan Gruber and below is her response. It is very through and should help.

Trey,
The short answer is "not to worry". The ivy will root into the bark but will not penetrate. It is not parasitic and will cause no direct damage to the tree. There are trees covered in ivy in some of the finest gardens in the world, and many have supported the vines for decades. If the tree is mature with thick bark I would keep the ivy and enjoy the beautiful effect. Just keep the ivy from covering smaller branches and leaves.
Now for the long answer. The roots will compete with the tree for nutrients and water, so be sure the tree has adequate amounts of each (again, if it is a mature tree and shows no signs of stress, these inputs may not be needed). Another concern would be that the ground cover often provides a home for voles who may knaw at the bark (at ground level). I have seen a multitude of young (under 8" diameter) trees die this way; most were just surrounded, not covered by the ivy. Finally, the ivy could mask the signs of borers and cankers...again, mainly a concern for younger plants.
Remove the ivy, if desired, by pruning the base of the stems and prying the ivy off. If the bark is being damaged in this process it may be best to let the vines dry up for a couple weeks before ripping. Herbicides can also be used on the ivy around the tree. A 25% solution of glyphosate can be applied to cut stems, OR in the words of the estimable Mr. Calhoun " try triclopyr" - a 4% solution.

Again, thanks for the question and let me know if you have more.

Respectfully

Trey Rogers, The Briggs & Stratton Yard Doctor, YardDoctor.com