I took a closer look at the ivy growing on the tree and all along the fence line. The good news is that it looks like English ivy. The non-poisonous kind.
But that doesn't mean that poison ivy might not be lurking there.
The bad news is that I really can't go all willy-nilly with the Round-up because that will kill everything. And while I really don't want ivy all over the place, I would rather be organic in its removal than getting all nuclear about it. Because I do want to eventually grow things there and I don't want to poison my dog.