I submitted an LOR online for a student to a US school. Student claims they want a physical copy. How should I respond?
It's completely possible a school might ask for an original letter on paper sent direct to them.

It's been identified as a US school but not which one.  There are perhaps 600 graduate institutions in the US.  Multiply that times the number of programs.  There simply has to be some variance in admissions policies.  At any particular school, it's completely possible they have an admissions policy of auditing LORs by asking for paper copies of all or some subsets of those submitted electronically.  There's no national standard on this kind of thing.

(I was surprised when University of Washington wanted paper originals of my own LORs for my first faculty appointment a few years ago.  So I figure there have to be schools that might want paper originals for student LORs.)

If you're unsure of the authenticity of the request, you might ask to see the communications the student received.  But once satisfied, I'd try to comply.  (I keep copies of the LORs I write so I can resend them with a new inside address when a student applies elsewhere; I assume you do, too.)

I would, of course, only accept a request for an original sent direct to the school. A request that the original be given to the student for delivery to the school would ring bells as bogus and likely end the need for any new LORs for that individual.