Quantifier-Negation sentences allow an inverse scope reading in Tibetan but not in Chinese. This difference can be attributed to the underlying syntactic difference: the negation word can be raised at Logical Form in Tibetan but not in Chinese. This study investigated whether Chinese-dominant Tibetan heritage speakers know such difference. We conducted a sentence-picture matching truth value judgment task with 28 Chinese-dominant Tibetan heritage speakers, 25 baseline Tibetan speakers and 31 baseline Chinese speakers. Our baseline data first confirmed the difference between Tibetan and Chinese: the inverse scope reading is allowed in Tibetan but prohibited in Chinese. Our heritage participants' data showed a divergence: one group of heritage speakers allow the inverse scope reading in both Tibetan and Chinese while another group prohibit it in both languages. There is a third group of heritage speakers who are aware of the difference between Tibetan and Chinese. Our findings suggest that while it is possible for heritage speakers to attain nativelike knowledge of an interface phenomenon that differs in their two languages, they may also be subject to crosslinguistic influence and adopt one of two opposite strategies. Both strategies can minimize syntactic differences between their two grammars so an economy of syntactic representations in their repository of grammars can be achieved.