From the link: Unwarranted demand: A demand is unwarranted unless: (a) that they had reasonable grounds for making the demand AND (b) that the use of menaces i

From the link: Unwarranted demand: A demand is unwarranted unless: (a) that they had reasonable grounds for making the demand AND (b) that the use of menaces is a proper means of reinforcing the demand. i.e. the use of "menaces" needs to be proper. In this case, their contract is the proper means of enforcement. Digging up additional "dirt" not covered/mentioned in the relationship would be considered improper, and is therefore blackmail.