Use some of the green metal vinyl coated fencing that most of the home improvement stores carry. You can tack it to the wood fence with staples and it will be sturdy enough to allow you to pull the vines off the trellis in the late winter with no damage to the fence or the trellis. The fencing comes in 3 or 4 foot wides and you can place one section above the next on the fence to make it as high as your fence.

Here is a link to a similar question asked by someone else and pictures near the bottom of the post showing the green vinyl coated fencing on her fence.

Here is a link that might be useful: Previous post about trellis

Those photos look great. I like that idea! Thank you.