A single hash (and a couple of temporary hashes) cleans up the code somewhat at the cost of a higher degree of Perl knowledge for understanding:

use strict;
use warnings;

my $str1   = 'CHARLIE ROOT';
my $str2   = 'HARRY NODE';
my @chars1 = split '', $str1;
my @chars2 = split '', $str2;
my %hits;

$hits{$_} = 1 for @chars1;
++$hits{$_} for keys {map {$_ => 1} @chars2};
print $_ for grep {$_ eq ' ' || $hits{$_}++ == 1} @chars1, @chars2;
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Prints:

CLI TY ND
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