Before I post the code, I need to let you know that

1. yes, I know that HTML code should not be parsed with regexes
2. I only came across this problem when trying to solve this for someone else, but the regex question also applies to other examples

#!/usr/bin/perl
use strict;
use warnings;

my $string =<<'EOF';
<tr>
<td>aaa</td>
<td>aaa</td>
</tr>
<tr>
<td>NOTWANTED</td>
</tr>
<tr>
<td>bbb</td>
<td>bbb</td>
</tr>
EOF

# try to remove all table rows with NOTWANTED
$string =~ s/<tr.+?NOTWANTED.+?<\/tr>//gsm;

print $string;
[download]

prints only the third table row. As far as I understand, the problem here is that regex starts with the leftmost "<tr" (the first one) and will find a (smallest) match that contains NOTWANTED and will remove it.

While this problem can easily be solved with

my @tr = split(/(?=<tr)/, $string); # split at <tr, but do not remove 
+<tr
@tr = grep { ! /NOTWANTED/ } @tr;   # remove the elements with NOTWANT
+ED
print join('', @tr);
[download]

I'm still curious if it can be done with a regex replacement.