@extrabio1947
The programme was 'Drain the Oceans,' Ep 2.2: 'Secrets of New York'
link
The pewter button was in fact to the 52nd Regiment.
Curiously, Dr Warren Reiss (Univ. Maine) the Marine Archaeologist, for some reason identifies the 52nd as a unit of "grenadiers, very aggressive, assault troops."
Perhaps he was confusing grenadiers with light infantry ('the other flank'?) given the role of the regiment's Light company in Maitland's notorious 2nd Light Infantry or perhaps even their subsequent 'Napoleonic' exploits in the Peninsula and at Waterloo.
However, the programme takes this ball and runs with it, suggesting that the sunken vessel had been a lighter ferrying prisoners to the hulks off Brooklyn, "crewed by British grenadiers"- "the most fiercesome troops in the British army."
Probably not the most likely role for British 'shock troops,' whatever the regiment, while the 52nd battalion coys spent little time at New York, being part of the garrison of Rhode Island from November 1776 till 1778 when the depleted regiment was drafted and raised anew in England.
A shame none of the team belonged to TMP. Somebody could have put them right. Smiley speccy face. }8^)
A remarkable archaeological discovery nonetheless, given its location.