I actually made a much worse mistake when interviewing for the job I currently have (I booked the plane ticket for the wrong month), and paid a few hundred dollars out of pocket to make the change. I don't actually think it would have made a difference, but I was honestly too embarrassed to even try to ask for it.
The risk/reward difference is such that it's probably better to just keep your mouth shut, but I do find the other answers oddly ignore a crucial issue: there is no unitary "they" who is both making a decision about your job and the reimbursement. Of course, it comes from the same institution, but not really the same people. Your reimbursement will probably go directly to a secretary, and be signed off on by the chair without her/him even really looking at it. At my own institution, I doubt anyone would even notice if you sent in both receipts (maybe the secretary would think it was odd for a moment, but s/he has other stuff to worry about). Of course, there is some chance that it would be questioned, or go over some limit, and then maybe the secretary would mention it to the chair (or the chair might notice the bill being unusually high), and maybe the chair would mention it to other people in the department. That is the risk.