This isn't a "trick". They're flat out asking if the person wants to do that and can only take action with their permission.
How kind of them! Because we were all taught in civics class that when you sign a petition, you should be prepared for some faceless political committee to just wipe your name from it if they don't agree with the petition. North Carolina Democrats are kind enough to ask you if they can wipe your name, because they just love democracy that much!
So when they ask don't say no and it won't happen. Where's the problem?
Nothing! Like I said, every time I sign a petition, I expect a faceless political committee to weigh in on whether I meant to sign what I signed. This group goes the extra mile and does the favor of asking me, "hey, your signature is on this, did you sign it, and did you mean to sign it?" As I always say, democracy is best when faceless political committees lend a helping hand and chaperone your participation, just to make sure everything's going all right!