Moves are dramatic, and happen at a dramatic pace.
Talk it out and find a place where you agree on the uncertainty, then make the move that makes sense.
-- Masks p.34, "Triggers and Uncertainty"
The sentiment's common among PbtA games - moves don't happen unless everyone at the table agrees that the appropriate fiction has established what move should happen and for what stakes.
Rejecting someone's influence over you is almost necessarily a dramatic beat, and like every other move has to happen at an appropriate place in the fiction.
If someone tries to use Influence to shift your labels:
That move itself gives you a dramatic opening to either accept the shift or take the risk to reject that influence.
If someone leverages their Influence into +1 ongoing against you:
If you want to reject their influence, the proper time to do it is before they make the roll, rather than trying to "change the past" by affecting a roll that's already landed. So, to follow the book's example:
when Hornet tries to provoke Sureshot into coming with her on a mission instead of moping in his room
Sureshot and Hornet are both fairly equal participants in the scene of Hornet trying to wheedle Sureshot to come out on patrol. If Sureshot wanted to reject Hornet's influence so it was harder for her to provoke him, I'd allow that as long as he could come up with an appropriate response, like shutting the door in her face, and resolve his roll to reject her influence before she makes her roll to provoke him.
It's possible someone can leverage their Influence over you in ways you might not be able to respond to - for example, if they're Assessing a Situation that revolves around you but you're not aware of them. In that case you don't have much ground to reject it.
If someone surrenders their influence to change a roll or give you a condition:
Inflicting a condition works under the same caveats as leveraging influence - trying to inflict that condition is going to mean personally involving that influence in a moment of drama, and you probably have enough dramatic time to reject that influence if you want to take the chance.
Nudging a roll after the dice have hit the table is a very unusual thing to happen, and necessarily is less of a spotlight moment than whatever it was that caused the dice to go tumbling in the first place. Especially if someone's burning their Influence after they already leveraged it against you, trying to work up the drama to reject that influence in the moment usually doesn't make a whole lot of sense.
That said, sometimes it does, or it might? If there's a really important dramatic juncture that someone is looking to burn Influence on to nudge the roll downward, you might feel like there should be some uncertainty how that's going to turn out. Like, say, Rex wants to burn his Influence over Grasshopper as she's trying to Unleash Her Powers to capture the shady government conspirator that transformed him in the first place, because he's afraid of what will happen if she does.
In that case, what might work better is looking at the Defend Someone move to see if it fits. It almost certainly will, and the numbers on defending against a PC threat line up with the effect of burning influence.
If you're responding to a move in a way that suggests you're rejecting Influence:
Even if Sureshot doesn't try to reject Hornet's Influence before she rolls Provoke, anything about the events of the succeeding mission might still cause him to regret how easily she talked him into it and take actions to reject her Influence. But the Provoke roll's in the past, so nothing about it changes as a result.