Static Target Numbers
A character can spend a bennie to reroll at any time, before the result of the roll is made. Once that result is declared, the roll’s result sticks.
Due to the volatility of an opposed roll, either side is able to use bennies to reroll up to the declaration of the victor. Any reroll is made against the current number set by the opponent, a reroll does not grant or force them to roll again. Once the victor is identified, and any results are applied, the reroll cannot be attempted.
With either situation, a degree of tolerance should be allowed. Often, rolls are quickly made, addressed and moved on before one has the time to decide if they wants to use a bennie to reroll. Please keep this in in mind, and allow some leeway if little to no opportunity is granted to resolve this.