Thank you for the great tips!
Oshyan, I'd rather cut off my right hand than using Photoshop for this problem
!
Thanks, jamfull, this could work. But in the meantime I found another solution: I masked out the area where the weird reflections appear by a painted shader. Not really elegant, but effective, and it makes me feel much better than cheating with Photoshop.
Before I try jamfull's fantastic trick, I'll see, if the reflective shader looks the same in the image with ray traced reflections unchecked. Then I could try again to uncheck "specular highlights" in the blue light's settings.