As others have already pointed out, there's a better way. That said, the reason your code fails is the grep isn't doing any kind of test. You want to actually check whether $hit is among the elements in @group1, not whether it is itself true or not.

use Data::Dumper;

my @group1 = ('A','B','C','D','E');
my @group2 = ('F','G','H','I','J');

foreach my $hit (@group2) {
    push (@group1, $hit) unless grep { $_ eq $hit } @group1;
}

print Dumper( \@group1 );
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Output:

$VAR1 = [
          'A',
          'B',
          'C',
          'D',
          'E',
          'F',
          'G',
          'H',
          'I',
          'J'
        ];
[download]

As long as we're pretending hashes don't exist, I'll mention also that List::Util has a better function for testing list membership called first. It's similar to grep, but it will stop searching as soon as it finds a match.