A bit more elegant, IMO:

use strict;
use warnings;

use List::Util qw( any );

my $text = 'f000124_90181234_dp';
my $sites = [ '018', '324' ];

sub delete_me {
    my ( $str, $aref, $anchor ) = @_;
    return any {
        index( $str, $anchor . $_ ) != -1
    } @$aref;
}

if ( delete_me( $text, $sites, '_9' ) ) {
    print "To be removed...\n";
}
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