Described in the Community Dances Manual, book III as being the English version of "Strip the Willow". In this instance, the "Strip the Willow" is refering to the Scottish dance rather than "Strip the Willow" as a figure.
Here the bold shows the words 'as published', the notes and annotations hopefully make things easier.
The strip the willow figure goes back a long way, there's a reasonably clear description in Trenchmore, published in the 2nd Edition of Playford (1652). The third part of which is:
Which is, perhaps, a description of the man stripping he willow down the set followed by the woman stripping the willow up. Trenchmore can be also be traced back quite a bit further