Ok, get it now. I don't think we are talking about a 'bias' here: you fear that the ranking of your Ph.D. granting institution will not play in your favor with industry; if you get a Postdoc at a higher ranked school, will this help in industry? And does ranking at the graduate level matter in industry?
As a Ph.D. (PostDoc), and in many industries, you rarely come in through HR. It's probably more common to rely on contacts, friends, academic collaborators, and recruiters. This already somewhat dampens the impact of where you studied. If you hope to get in through HR, expect trouble. What I say next assumes that you largely stay near your field of study (you're not a biologist seeking to do momentum trading).
Not quite dissimilar to JeffE's answer to a related question, at the PostDoc level you are expected to have some research to show; and as you probably won't show it to HR, the people you talk to quite possibly understand what you did, or maybe even are familiar with it. They also might know, or have heard of, your PI, which you mention as well you wonder if they do. A famous alma mater is certainly nice, but it will matter much less than how highly they think of what you did, and how it fits into your possible job there.
Applying as a Ph.D. (only) in industry will put much more emphasis on your graduating institution: in many fields, even if you publish, it might not yet be printed; and the breadth and number of your contributions tends to be naturally fairly small. I think hiring, in industry, based on name makes more sense then; but your field of specialization, and what you did, still matter quite a bit.
Finally, the further your potential job is from your field of expertise (and that is common too: I've seen people go from CERN to building user interfaces), the more names matter - as is probably no surprise to you. It also matters in just making people curious about you - in the stage of getting an interview; whereas what I wrote before is you discussing a job at a desk or lab.