ex gratia
adjective or adverb
                                                                                                                            
                                                            ex gra·tia
                    
                                                                                                              
                                                                                                                                  (ˌ)eks-ˈgrā-sh(ē-)ə  
                                                      
                                                          
            
                                
              
          
                                                      : as a favor : not compelled by legal right                                      
              
                             
ex gratia pension payments
                         
                
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  Merriam-Webster unabridged




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