actually, if they are stealing from your site with a hook on the link, no matter what, this is fraud. Take them to court sister! Not only is it damaging your image, but regardless of their name, this is an infringement of benefits as well as Copywrite laws.

My two cents - reiterated -
1) I'd definitely remove the live link you have using the very location in your link. That alone is providing link juice to their site.
2) I understand that Te Puke is the name of the town, so, no, I do not believe you can do anything about their use of the town name, but you can use "kiwi corral" in your keywords on your site.
3) You can keep on differentiating your site because they truly do not look similar.
4) You can purchase similar domains or partial name domains to theirs and build them out as mini-sites (legal? yes - unless and until you were to receive a cease and desist order depending on any trademark infringement which I doubt anyway. There's no way they're going to legally trademark the word "kiwi." It's a fruit.
5) You can state on your site "not to be confused with kiwi corral." if you truly feel that they are confusing potential customers.
6) You can ask for and list genuine testimonials from your customers.
7) Go to kiwi corral, as a guest, and acquire info to a) further differentiate, b) build knowledge to compete more effectively.
8) Apply and obtain any type of "official" seals such as the Better Business Bureau or similar in New Zealand. Also, conduct research to read more about their services / complaints.
9) Keep reiterating that your service is "personalized" for a better backpacking experience, etc..
10) As another member mentioned, keep on providing good relevant content and focus on your readers/customers. You may even offer a discount code to entice new customers. Post it everywhere especially on mini-sites. And, if they run one, you can state you will honor theirs.

In short, you can either ignore them completely, or compete better. This is business. And, no, there is nothing you can do to prohibit them, or anyone, from using the location / town name in their marketing or seo efforts.

I've never heard of this and don't like the sound of it. I not sure what to do about it, but I would report it to google. Kyle or Carson should have the answer if you can't find it here.

Just a thought, have you thought about doing the .co.nz add it as a sister site link the two. Just a thought.

I know that some of our ambassadors would know how to help you with this. Maybe send some pm's asking for advice.

Differentiate from them and just keep focusing on your niche. Google love good contents. Keep writing.

Give better service. More personal service. Big company can't give that.

There is a way out...check this link as it is very helpful.
http://www.entrepreneur.com/article/226140
When Business Names Confuse Consumers: The Basics of Trademark Law
Good luck!

Use theirs? They have a hostel, it is nearby the Puke, and they are called Kiwi Corral, and you can book a bed as backpacker. I don't see anything wrong in it. Perhaps your businessname is to global? I guess you can't claim the name The Puke, neither can you claim the name Backpackers

No very ethical sorry I do not have the experience to give you a solution I take it they have done an article that picks up your traffic as when you click it takes you to a different url kiwi corral

I'm just wondering. I'm thinking as to whether it's possible to report this to Google and explain what has happened?