What is background binding?
Background binding in this case would be the extent to which two proteins associate together by chance.  

A hypothetical example: you may have a mitochondrial protein import complex.  Usually cases there is a specific peptide sequence the import complex binds to , but proteins without an import peptide sequence will occasionally be bound to the import complex.  This is called the background binding for the protein complex.  The experimentalists might have measured this by cutting the import peptide sequence off a mitochondrial protein for instance.  

Any candidate would have to bind to the complex more than the background case to be considered a target for mitochondrial import.