The Steam game wants an Origin key from me.

Hi,

I bought Battlefield 3 on Steam and after selecting the server it gives me an error to enter the game key, see attached photo. I have already tried a lot of advice on the internet, such as deleting the file, reinstalling, just about everything and it still doesn't work for me. Of course, support doesn't respond, so I'll try here. If anyone is struggling with this, has struggled with it or knows how to solve it, I would be very grateful for the advice. Thank you :)