Potter's publishers, in defense of strong global copyright, would say that works like Tanya Grotter are theft, and such theft destroys the incentive to write in the first place. But the incentives argument is surprisingly unpersuasive in the international setting. To say Rowling will stop writing for fear of international parody is a difficult case to make. Only the most famous and lucrative works are parodied overseas. If an international adaptation is a sign you've made it rich, how can it be a serious financial deterrent for new writers?
The truer complaint is that Potter's overseas competitors may mean slightly less profit for Rowling and her publishers. It is also true that Burger King means slightly less profit for McDonald's. You could say that Burger King and Wendy's stole the idea of a fun, plastic burger joint from McDonald's and are unfairly profiting from their evil deed. But when it comes to burger joints, we accept that the consequence of a competitive market is less profit for the first mover (McDonald's). Copyright should be no different. So long as it provides Rowling sufficient incentive to write, it should strive to maintain as much competition and facilitate as much international trade as possible.
It is also true that these rip-off works make authors angry and may tarnish the reputation of the character. But what makes authors angry is precisely what they are least likely to write, and therefore often what copyright needs to permit. For example, in 1989 the rap group 2 Live Crew recorded an obscene version of Roy Orbison's song "Pretty Woman." Orbison's "Pretty Woman" became, successively, "big hairy woman," "bald woman," and eventually, "two-timin' woman." There was little question that it made Orbison's estate angry, tarred the reputation of the original, and was a commercial competitor that threatened Orbison's profits. But the U.S. Supreme Court found it a parody: a non-infringing fair use. The faux Potter books are not quite parodies, but they're similar. Just as refusing 2 Live Crew permission to parody would have destroyed the market for parodies (since authors rarely parody their own works), so Rowling's campaign destroys the market for international follow-ons, since Rowling could never write a Potter book that could capture the Russian spirit the way Grotter does. Rowling is using the cudgel of international copyright not to destroy something she could have created, but to destroy something she could never create.
In the end, few people are likely to mistake Tanya Grotter for Harry Potter; it is akin to mistaking Burger King for McDonald's. The international copyright system is justified in preventing the most basic forms of piracy. But it doesn't need to stop works like Tanya Grotter. The original Harry Potter is good enough to compete with its foreign cousins. So let a hundred Harrys bloom and let a hundred schools of magic contend.