Can a 3.33 Finance Major GPA hinder my career in banking?

If you have connections you should be fine. People generally refer to the sub 3.5 being a hindrance if you are trying to break into banking without connections. Just get more experience this summer, make sure to network a bunch a UBS, and keep improving the grades. Once graduation roles around you should be good with your connections and previous experience (especially if you are at Northwestern).