A "looser relationship" means a connection between two people or things that is not as strong or strict as it could be. It suggests that there is flexibility, freedom, and less structure in the relationship. Full definition
«The Leave campaign is going heavily on migration because most of the arguments they've been putting forward have been shot down by anybody with any knowledge or experience,» he says, adding that the recent rhetoric on migration bears «a very loose relationship with the truth». (totalpolitics.com)