There is no need to increment a counter to keep track of how many elements are deleted from the array. You can simply get the size before the deletion, and substract the size afterwards to get the difference.

Here's how I would do it:

sub delete_field {
  my $self         = shift;
  my $delete_field = shift;

  my $before_deletion = @{$self->{_fields}};

  @{$self->{_fields}} = 
    grep { $delete_field ne $_ }
    @{$self->{_fields}};       

  return $before_deletion - @{$self->{_fields}};
}
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You may also want to check out Removing certain elements from an array, which has some neat idioms somewhat related.