What are the potential motives for an industry recruiter to want to know your PhD GPA?
Does this imply the position is more of an office drone position than a pure research position?
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In general it is difficult to tell whether a PhD student is a good researcher or not right after finishing his/her degree. Good results could come from a helping advisor, a lucky topic, or good office mates. Bad results could come from bad luck, lousy preparations of the topic before the student toke over, and so on. GPA is at least somewhat objective.
By the way, industry research most often turns out to be much different from academic research. This might be good or not, but be warned.
While this may sound ridiculous, some employers do care about the GPA obtained during the PhD. I know that one of the contractors I worked for had an explicit requirement for undergrad and grad degrees, and hiring managers who wanted to make an offer to individuals with lower GPAs had to go through extra hoops to get it approved.
I would not stop the conversation with the recruiter solely based on this aspect. Maybe they really rank the candidates on PhD GPA (which is as irrelevant as ranking on height, mass or their ratio) or maybe the recruiter has to fill up a form which is not involved in the selection/ranking.
Try to learn what is the job about, what would be expected from you in the first six months and one year. Meet your future boss and be all ears on what he/she has to say. Make sure you actually want to work for them.
There is no such thing as pure research position. Both industry and academia offer research positions, where you have at least to manage other people, write administrative documentation, attend non-research meetings, teach your topic to individuals not interested about learning, teach uninteresting topics to equally disinterested people, etc.
In a research job, the actual creative work is 5%, and the rest of 95% is making the first 5% work, go through reviewers, obtain financing, manage contributors and disseminate it.
To add some more detail to @sevenseven's answer, remember that for most companies the recruiter is not an employee of that company. To answer your first question, the only motive they have is filling the position. GPA is a common thing to blindly ask on a laundry-list of questions they will ask anyone.
So, the employer likely does not care about your GPA; while it may be communicated in some way to the hiring manager, it's not going to be anywhere close to being a deciding factor. In my experience, hiring managers know that recruiters ask for this kind of extraneous info and are typically professional enough to know how to wade through all of it to get to the core question - "can this candidate do this job?"
If the job is interesting to you, continue through the process and provide them the GPA. In general, if you have (or are working towards) a PhD and interested in research type positions where there's a slightly higher chance they would care about your GPA, I'm assuming you have a pretty good one anyways.
Potential motives: giving them an easy way to weight one applicant over another.
Implications to the type of job: none.
Understand that many, many (, many, many) recruiters have no idea how to evaluate someone for a job, even though it is arguable that it is THEIR job to know how. So they try to find ways to do it that are objective and that can at least be argued to be relevant. Your GPA is arguably (though I wouldn't argue it) an indication of how well you performed in graduate school, therefore it is an easy way to distinguish candidate A from candidate B.
The hiring manager may or may not care, and may or may not even know the question is being asked. Unfortunately, arguing (as a candidate or potential candidate) that it is not relevant is not likely to be taken well, however right you may be.