Normally I'm big on using tr///, but in this case, the symmetry of cases suggests using a regex to filter out strings where any character is repeated too many times:

sub remove_poly
{
    my ($array,$lim) = @_;

    grep {
        my $max_num = int($lim * length())-1;
        !/(.)(?:.*?\1){$max_num}/
    } @$array;
}
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update: non-greedy for less backtracking; another update to include length checking for each element.