I have not found any whitening properties of tea tree oil but it can help prevent tooth discolouration and I have seen toothpaste with tea tree oil sold in shops.
Jain et al. (2014) states:
Tea tree oil’s major active component is terpinen-4-ol (30%–40%). This compound is responsible for its antibacterial and antifungal
properties [(Arweiler, et al. 2000)].