I doubt it is as simple as having it removed, removal of a tattoo is incredibly expensive and far more painful than the tattoo, sometimes costing up to 1000 per session depending on colour, placement and intricacy.
I highly doubt it has anything to do with the tattoo itself, is your friend certain that they are not merely connecting an unlucky period of time to the new tattoo, a lot of the time we subconsciously want something to blame for out bad luck or shortcomings.
You could try a cleansing, but what kind of bad luck have they been having, physical ailments, misfortune, something else?
Was the person who did the tattoo trained to been be a tattooist? did they comply to safety standards when it comes to blood borne disease and the correct sanitary practices, although potentially unlikely could her concern of bad luck be due to an incorrect healing of the tattoo or potential complications?