Use the list interface for trees.
The current tree interface is very strange. In any decent file manager, the List field's interface would be used – it's a vertical list, allows modification of each entry easily, and allows multiple selection of them. Contrastively, the current tree interface uses a context menu to manage items which means that none of those features are available except multiple selection. Deleting items is impossible, and most importantly, after a few items have been selected, the bar provided becomes full.
It should use the vertical, intuitive layout of the list field.