To chomp all elements you could

chomp @$_ for @array;
# or
chomp map @$_, @array;
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However since you only want to chomp one of them

chomp map $_->[2], @array;
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But why add another loop if you can do it inline?

while (<FILE>) {
    next if /^#/ or tr/\t// != 6;
    chomp;
    push @array, [ split "\t" ];
}
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Makeshifts last the longest.