I have a profile on AO3 where I say that I'd love if it folks remixed my stories or whatever, and all I ask is that they let me know so I can see the finished products. People do get inspired, and I know I'd be upset if I saw something I did lifted wholesale. But what I hope is that the new work transforms the idea. If it isn't a transformative work, then it falls under plagiarism. But we're all fic writers, and what we do is transform, right?

If I see something that inspires me, I let the writer know as soon as I'm making my notes for what I want to write, and I ask if they'd mind. For example, I read a fic in an entirely different fandom that was a crossover piece. As soon as I read it, I knew I needed to write my own fusion of that crossover world with HP (it's a WiP and I swear I am going to finish it this summer if I have to make a fest to make myself do it). So I dropped a note to the original author, and was very pleased that it made them smile and they were all for the idea. I'd hope someone did the same for me.

On the other hand, there are those instances where you get ideas independently, then feel awkward, like writing a fic framed around an event, and when you go to post it, realizing there's another fic, same pairing, framed around the same sort of event, and then you worry that you've inadvertently hive-minded and copied the idea. Or that may just be me feeling weird about such things.

I think, in the end, it depends on what piece you want to take into your own work. Like vaysh11 says, how specific is the idea? In any case, though, I think notification isn't just polite, but might make the original author smile. After all, don't we all like to know that we're inspiring to others?