Wikipedia says it's been Iranian/Omani territorial waters for quite a while:

> In 1959, Iran altered the legal status of the strait by expanding its territorial sea to 12 nmi (22 km) and declaring it would recognize only transit by innocent passage through the newly expanded area. In 1972, Oman also expanded its territorial sea to 12 nmi (22 km) by decree. Thus, by 1972, the Strait of Hormuz was completely "closed" by the combined territorial waters of Iran and Oman.

The Strait may well have some, but the traffic separation scheme for shipping is absolutely in Omani territorial waters, and another part of traversing the Strait includes passing through Iranian territorial waters.