>It could be a transatlantic divide, after all.

if so, it's a recent transferral. here's OED2 (fwiw):
Stock Market (orig. U.S.).


[f. green a. + black)mail; cf. green n. 7d.]
The practice of purchasing enough shares in a firm or trading company to threaten a take-over, thereby forcing the owners to buy them back at a premium in order to retain control of the business. Freq. attrib.
1983 National Law Jrnl. (U.S.) 21 Mar. 23/4 Corporations are scurrying to combat a perceived threat from those professional investors who practice ‘greenmail’—putting pressure on a company to get a buy-out for cash. 1984 Daily Tel. 16 June 17 The Disney settlement is the latest and biggest in a recent spate of ‘greenmail’ deals. 1984 Times 15 Oct. 17/6 Two leading companies in the United States are introducing schemes to help ward off the threat of unwelcome takeover bids or attempts of ‘greenmail’. 1986 N.Y. Times 13 Nov. d1/1 CPC may have revived ‘greenmail’ by moving to get Ronald O. Perelman off its back, some Wall Street players contend.