Remove it: English Ivy is an invasive plant, and allowing it to climb not only aids in its spread (once mature after climbing for a while, it can flower and produce berries that birds distribute to more areas), but also can contribute to the death of trees. Do not pull vines off the bark, as this can injure the bark in the process. Rather, sever the vine's connection with the ground, and the stems left adhering to the bark will dry out and die (and eventually fall off) on their own.

Miri