This is a native deciduous, woody vine. We would recommend that you remove the Virginia Creeper from the trunk because as it grows it can deny photosynthesis to the foliage on the branches and hold moisture to the trunk area. http://extension.umd.edu/hgic/virginia-creeper
You can cut the vine at the base. The rest of the vine will dry up and die, at which time it can be more easily pulled out of the trees.
If you want, it is fine to leave the vine growing around the base of the tree.