Actually, worse might be that the pirate would send a DMCA takedown to your hosting provider. I've seen reports of this happening, from Indian firms no less.
PS: Just to clarify, the copied version of our website is hosted at: https://www.feedsapi.org [Article already updated]
I'm not sure they stole yet. They might be in the process of stealing it.
Distinction that doesn't make a difference?
ie: perhaps they never planed to use it as is -- a developer could have downloaded the website just to look at how it's structured, and it's an unfortunate accident that it ended up on the open web...