I guess it should be ok if you insist on paying and depending on your interviewers response, things get settled. I don't think a gift is appropriate at this point.
For which school is this interview.(Kellogg ??)
I have my interview over lunch on Friday. Was wondering about the etiquettes for the meeting like who picks up the tab(or people go 50/50), do we take a gift for the interviewer etc etc. Appreciate any inputs.