In the future please only post the relevant code. Trim your examples down to the minimal case that still demonstrates the problem. See How (not) to ask a question - Only Post Relevant Code

Here is a somewhat trimmed down version:

use warnings;
use LWP 5.64;
use URI;
use HTML::LinkExtor;

my $base = "http://search.ebay.com/ws/search/SaleSearch";
my $browser = LWP::UserAgent->new;
my $url     = URI->new($base);

$url->query_form(
    'satitle'=> 'learning perl',
    'sacat'=> 267,
    );
    
my %data = ();

# set up the link handler sub
my $link_extor = HTML::LinkExtor->new(\&handle_links);

#get search results
my $response = $browser->get($url);

#get the links
$link_extor->parse($response->content);

exit;


######################################
sub handle_links {
    my ($tag, %links)=@_;
    if ($tag eq 'a') {
        foreach my $key (keys %links) {
            #search for links with Viewitem
            if ($key eq 'href') {
                if ( $links{$key} =~ m/ViewItem/) {
                    #get the item number from the link
                    $links{$key} =~ m/item=(\d+)/;
                    
                    printf "links{%s} = %s\n",$key,defined $links{$key
+} ? $links{$key} : 'undef';
                    if (!defined $1) {
                        die "\$1 is undefined.";
                    }   
                    $data{$1}=$links{$key};
                    }
                }   
            }   
        }   
}
[download]

Output:

links{href} = http://cgi.ebay.com/Learning-Perl-by-Randal-L-Schwartz-1
+997_W0QQitemZ220021417901QQihZ012QQcategoryZ2228QQssPageNameZWDVWQQrd
+Z1QQcmdZViewItem
$1 is undefined. at test.pl line 43.
[download]

The warning is being printed because while $links{$key} =~ m/ViewItem/ matches, $links{$key} =~ m/item=(\d+)/ does not.

To avoid warnings like this you should always check that the regex was succesful before checking $1.