I think that the books are a bit unclear on whether one can modify the roll by Infamy Bonus after succeeding at the infamy test to roll on the Rewards table of a god. So, the question is: is one allowed to modify the Rewards roll by their IB?

You may alter the Gifts of the Gods table result by your Infamy bonus, but not the result on the Rewards of Chaos table.

While technically true, don't forget that its your game. If you want to let the players have an itsy bit more say, have fun

There is also an optional rule on page 29 of the Game Master's kit that allows you to burn infamy to alter your Rewards of the Gods roll by sacrificing half the infamy amount by which you want to modify the Rewards of the Gods roll.