If its a preexisting structure AND directly on the property line, then they should have gotten your permission to alter it. But the likelhood of it being directly on the line is small. You would need an exact survey to tell. I would try to keep peace by just asking if you can paint your side.
I had a slightly similar situation recently. My neighbor came over and informed me they were replacing the fence around their property. Their current stockade fencing was right up against my chainlink fence. Also they were extending the fence to the curb which meant removing an old piece of rail fence and some foliage on my side. The even offered to take down my chain link at their expense. I was agreeable to all this, but when they workmen were taking down the fence, I had then leave one post at the end that was opposite the corner of my house. This served 2 purposes, first it marked the property line so they couldn't expand their yard by putting the fence on my property and it left a post if I wanted to put up a gate. Now that side of my property has a nice fence on it
