I wouldn't just toss it. I think that might escalate issues more with her. I'd go over and ask her how much longer she is needing to leave the tarp there since you are concerned about it causing rot or discoloration. If she says indefinitely or another month it gives you an opening to reply "that won't be possible. You might not be aware but that is my fence. I paid for it and I don't want a tarp hanging on it for that long. I'd appreciate if you go ahead and move it tomorrow."
Bold above is an excellent "approach" point. It is a wood fence.
Send DD's BF over to ask her to take it down.
Oh, my. Am I bad for really giggling at this? I am sooooo tempted! Can I? Can I? Huh?
But probably not the best way to handle the situation (although he would do it in a heartbeat.)
I really don't want to just throw it over the fence. That sounds like retaliatory rudeness . . . I did think about it, but posted here instead.
Folding it up and putting it on her doorstep? Due to some of the responses in the wind chime thread, I'm hesitant to touch NN's property.
Just because NN doesn't talk to you OP is no reason why you can't talk to her. How she chooses to respond to your speaking to her politely is her issue, but at least you'll know you took the high road.
That's a great point, WillyNilly. Thank you for giving me the spine I needed.
Although, talking to her will have to wait a few days or more. We're having a pretty bad rainstorm here (dropping down to freezing then upcoming snow.) Asking her to remove it while it's still wet/frozen is probably not a good thing, right? Or did I just loose my spine?
Thank you, everybody, for your responses. I've never had a "cold/bad" neighbor before, so I wasn't sure how to handle this.