If you are refering to one of the invisible dog fences that use buried wire. They are really nothing to take down. The wire can be cut where it exits the ground. The rest will not hurt a thing being left buried. Trying to pull up the wire up. You may run the risk of distrubing sod that covers the wire. How much of a distrubance it may cause will denped on how wide and deep the trench was dug to bury the wire.
Leaving the wire will also allow the homeowner the option of using the fence again at a later date. With the wire already buried. They will just need to splice into it in order to connect to the sending unit.
By now, I would have run over all of them trying to get close...line trimmers knock then down as well. If that dog hasn't learned by now, she should get rid of it...LOL. A month or so is usually only needed with the flags up marking the line.
those flags are a PITA. If a lawn has those "Miss Dig" flags for burriied cables, I simple avoid them totally. Like GrassFearsMe said, they can be dangerous and not to mention time consuming to trim/mow around.