These aren’t bulletproof but can work in addition to having the negative review downvoted (#6).
1) You can OVER refund. Amazon allows you to refund up to $20 over the amount customer paid. You cannot over refund and “demand” a change. You can only “hope” they feel guilty and remove or update their review. I’ve heard of this working with about 30% positive results with over refunding and writing a nice email without ever mentioning they modify their review.
2) You can call them, if you can find their original order and phone # which is sometimes possible. If you are good on the phone, this can work. I’ve heard of some good results from doing this as well.
3) You can obtain a boatload of 5-star reviews and bury the negativity with a bunch of positive reviews.
4) In very select cases, you can add a COMMENT on a review. This would be something you’d rarely do as it depends on the nature of the review. You wouldn’t want to add comments unless it’s extremely well thought-through and expertly presented as you can leave yourself open to having this backfire. Here is a basic example: Respond to a negative review with a nice message letting them know you’ve been very careful to do “x.” In this example, it is difficult to quantify what “x” is without knowing your specific circumstance. However, basically, you may wish to use this as an opportunity to politely point out why their review is not accurate (making sure to not be defensive). You want your reply to be both apologetic AND informative. So, that allows for a little bit of gentle correction without appearing overly defensive or thin-skinned. It is a fine line and we can help you with that nuance. Make this a public response so that everyone sees you are standing behind your product. Offer to provide a refund if they are truly not satisfied. State it has a money back, lifetime guarantee. Your response is an opportunity to let everyone else know you are a real company, you are responsive, want your customers to be happy, etc. This isn’t really “to” this complainer, but a great opportunity to highlight your quality and top notch service.
5) You can make a case to Amazon, but it’s VERY hard. They do not even follow their own policy. But if you have a strong case, or can prove something odd, it occasionally works.
6) If you can get a substantial number of “NO” votes on a review, that may “HIDE” the review. I’ve heard it takes over 100, but I’ve never been able to actually see this work even though I’ve seen the “hidden review” mark on a few listings. I like number 2 as a first effort since there is no harm in it. I like 5 and then 3 after that.