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I scheduled an interview about a month ago before my second semester grades were out. Before my interview, I received my grades and they dropped a little. But I didn't have my updated class rank until after the interview. They did not ask me for an updated resume with new grades before the interview or during the interview.

Should I have given them an updated resume with my new GPA before or during the interview even though they didn't ask for it? If my GPA had been higher I would have wanted to give them an update, but given that it was lower I didn't want to. Any concerns about this?

if you are at the interview stage, you are there to interview for fit. Giving them an updated resume is proper, i doubt they'd care about a small slip in grades, which fluctuate all the time. Stop worrying about grades and nail that interview