It’s a very interesting one. Bahrain was part of Safavid Iran for over a century, between approx. 1601-1720, after the Portuguese were driven out of the islands (having occupied it for some 80~ years). This is a fascinating period of Bahraini history, immensely undervalued today because of Iran/Saudi tensions and Bahraini national history essentially being taught as though nothing happened between the birth of Islam and the conquest by the Bani Utub (Al Khalifa) in 1783, but I can recommend a few articles/books later. The Safavid Bahrain era ended when Oman occupied the islands, and the empire collapsed just a few years later and never managed to reassert strong state control. In the violent 50-year game of musical chairs that followed, the Iranians managed to assert a loose vassal relationship over Bahrain, which ended when the Bani Utub conquered the islands.

However, this era of direct rule wasn’t the basis of the Shah’s claim. His claim actually goes to the entry of the British empire in the region; they come on the scene in the early 1800s on the pretext of ending ‘piracy’ along the sea route to India, and quickly established themselves as the biggest player. I wrote about the incident in a blog a few years ago:

in 1822, he (the British agent) concluded a legal agreement with the governor of Shiraz recognising Persia’s right to Bahrain as a territory. The Government in Bombay reacted swiftly, voiding the agreement and firing Bruce from his job as Resident. Bruce’s rogue actions left a stormy legacy on Bahraini politics, contributing directly to 150 years of Iranian claims on Bahrain. These claims, which hinged on this agreement as proof of their legitimacy, were only dropped in 1970, continue to haunt Bahraini politics to the present day.

This British agent was acting beyond his orders and was punished swiftly for it. But this was the basis of the Iranian claim, raised first in the 1920s at the League of Nations and in the late 60s, in the incident you mention. In essence, the Iranian claim rested on the argument that the British Empire recognises Iran as the rightful owner of the islands, rather than on the actual formal control that ended 250 years prior.