Thank you for your reply.
I tried it again, and made better notes. My archive is td.cpio:

$ cpio --list -i <td.cpio
.
t2
t1
t3
1 block
$
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My script is

#!/opt/ActivePerl-5.12/bin/perl
use Archive::Cpio;
my $cpio = Archive::Cpio->new;
$cpio->read('td.cpio');
$cpio->remove('t1');
$cpio->write('tdnew.cpio');
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The output tdnew.cpio is identical to td.cpio

I think the answer is in the Archive::Cpio code. The entry should be removed in

sub remove {
    my ($cpio, @filenames) = @_;
    $cpio->{list} or die "can't remove from nothing\n";
    my %filenames = map { $_ => 1 } @filenames;
    @{$cpio->{list}} = grep { !$filenames{$_} } @{$cpio->{list}};
}
[download]

I cannot decipher that last line but I do not like it (I may be completely wrong).

How can I get this right? Thank you.