First, noise does tend to scare bunnies that haven’t been raised to it. A bunny in a room with a loud TV will learn to ignore it, and one raised in quiet will be sensitive to any sound near or far. Please know that a bunny’s hearing is 10x better than a human’s. (Those big ears really work!)
I totally agree with MD. I would like to add that if your parents have made this offer in order to get you to sign on for a portion of the responsibility, then the offer of doing more chores is just right. Actually, they may be wanting you to take charge of the bunny’s care, such as daily feeding, supervised exercise, and frequent litter pan cleaning. The bunny has provided you with extra chores that must be done, and if you are willing to do those, you will be responsible for the care of your pet and it won’t fall to your parents. Maybe that’s what they have in mind.
But they are as responsible for the health and well-being of any pet of any underaged child in their household. Since you are not yet an adult (please don’t tell us your age here.) they need to take the lion’s share of the financial expenses – buying the food, going to the vet, setting up the habitat. I hope they will be honest with you about what exactly they expect you to share in that, and if they are not prepared to do that with you or for you, then yes, rehome asap before you and your bunny are bonded. Did they give you the bunny or did you bring it home and surprise them?