Why would you think that bloat needs to be corrected? The goal is not to pack the most functionality in the fewest lines of text. It is to produce a program that works and can be read.

Now that the flame-bait is out of the way, that for() loop should be a foreach loop so you can drop the $itr variable, warnings should complain that $r is not used, the my declaration for $lk should be moved inside of the loop to localize it as much as possible, and $_ does not need to be assigned to in the map. Lemme see, that gets you down to this:

my %UHash;
foreach my $pic (@Linked_pics) {
    # Meant to pick the filename out
    my $lk = substr($pic, 1 + rindex($pic, '/'));
    $UHash{$lk} = $pic;
}
@Linked_pics = map {$UHash{$_}} sort keys %UHash;
[download]

Oops, I accidentally made it shorter. And clearer. In fact so clear that it is now obvious that if the format of the URL changes, your code will break.

I will let you fix that for yourself.