  Every null-homologous link in an oriented 3-manifold is isotopic to the
boundary of a ribbon of a Legendrian graph for any overtwisted contact
structure. However this is not the case if the boundary is required to be
non-loose. Here, we define the `Tight Reattachment Property' for a Legendrian
graph and show that it implies the boundary of its ribbon is non-loose. We also
discuss the applicability of this property and examine examples and
constructions of Legendrian graphs with this property.
