That was 'The Two Sisters', Jack.

The phrase in question wasn't especially common in tradition, and seems mostly to have been restricted to versions found in Aberdeenshire (where there is always the possibility that Peter Buchan's influence may have played a part in 'standardising' oral versions). Its popularity nowadays is probably largely down to recordings made by Ewan MacColl and others, from which a lot of people have learned the song.

In the relatively small number that do use it, it occurs as 'the lindie', 'malindie', 'the linsie', 'the lindsay' and so on. Pete Shepheard (sleeve notes, Ye Shine Whar Ye Stan: Jock Duncan. Springthyme SPRCD 1039, 1996) glosses 'lindie' as 'the linden or lime tree'; others have made the same connection, and it is one possibility.

Annie G Gilchrist (Journal of the Folk-Song Society VII (22) 1919, 82) conjectured that the ballad might have been 'brought to Britain by the Northmen' and continued, 'the "rose and the lindie" suggests a corruption of a Norse refrain in which the word "rosenlund" occurs - "rosenlund" (literally rose wood) according to Dr Prior (Ancient Danish Ballads, Introduction, p xxxvi) being the exact equivalent of our "greenwood," and, like it, the scene of many ballad adventures.'

Of course, that pre-supposes that Danish forms of the story are older than British; and Steve Gardham has pointed out that the song was not found in Denmark until 1870, 25 years after Grundtvig had published a translation into Danish of a version collated from several Scots texts. Another possibility, then, though it may well be an anachronistic red herring.

What does the phrase mean? Despite the ingenious and arcane speculation in which people love to indulge when such topics come up, the answer may merely be 'nothing in particular'. Such refrains don't need to have any function beyond euphony, and often turn up in other, unrelated songs as well, so there is no guarantee that the words they contain have anything much to do with the song in any case. If we need the refrain to mean something, then Jack's guess is as good as any, and has the advantage of being straightforward and logical.