Answer: Ivy can cause all kinds of problems when it is allowed to climb up tree trunks. It can hold too much moisture against the bark, leading to rot. It can cause splitting of the outer bark of the tree due to the shear force of the growing vines. If it's allow to climb up very far, it will become heavy enough to cause stress to the tree and it can act as a sail, catching wind and pulling a tree over. Add this to the potential of strangulation and girdling, and the facts indicate it is wise to remove ivy from the tree.
At a minimum, cut enough ivy away to expose the flare of the trunk of the tree where it meets the ground. It would be even better to remove the ivy within several feet of the trunk. After removing the roots and cutting the vines at ground level, pull what you can from the tree. This might mean that you'll have to cut the intertwining vines and pull them off in pieces. Anything you can't reach to remove (including the disc-like pads), will eventually weather away. Don't worry too much about removing the pads -- they won't produce new plants. And, unless a piece of an ivy vine has gotten a foothold in a crevice or other moisture holding spot on the tree, the vine should die off after being cut at ground level.
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