Untested:

my %allowed = ( u => 1, i => 1, b => 1);
my $text = "";
while ( my $token = $p->get_token ) {
    if($token->is_text) {
        $text .= $token->as_is;
    } elsif($token->is_tag && $allowed{$token->get_tag}) {
        $text .= $token->as_is;
    }
}
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Now you can filter your text in $text, for example like:

my @match = grep /$lookup/, split /\n/, $text;
print "$_\n" foreach @match;
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There is, of course, the chance that you'll match on the tags now.