Here's a solution that keeps retains the original order and the original case. Basically, it removes any later occurrences, regardless of case, but keeps the case of the original.

print join ", ", unique_case(qw( THIS This That That 
                                 ThAT ThAt ThAt THIS
                                 These Those ));

sub unique_case {
  my %seen;
  return grep {!$seen{uc $_}++} @_;
}
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