I typically make A or A+ for Time and Offense, but I don't always make the best grades for Finesse. Furthermore, I get straight Ds when I run from fights during my all-night runs to level up Survival. How do my report grades affect me? Am I getting less EXP if my average grades are low?
Receiving high grades, you are getting some bonus experience, up to 40% (getting all grades A+).
Full breakdown of Finesse and Offense can be found here.
Since the Dec 22 2016 update, there are 3 new accessory items which reward additional AP for getting A+ grades in each category.