$URLFix = '&';
$parsedPayload->{results_link} =~ s/&/$URLFix/g;
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The "correct way to fix it" is to use an XML building module that automatically escapes things for you.

use strict;
use warnings;
use XML::Simple qw( :strict );
my $xml = '<foo><bar>blah&amp;blah</bar></foo>';
my @opts = (KeepRoot=>1, KeyAttr=>[]);
my $data = XMLin($xml, ForceArray=>1, @opts);
use Data::Dump;
dd($data);
print(XMLout($data, @opts));
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Output:

{ foo => [{ bar => ["blah&blah"] }] }
<foo>
  <bar>blah&amp;blah</bar>
</foo>
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Note that the ampersand is unescaped in the first output line, then escaped again in the XML.

Also, don't use XML::Simple. Someone want to suggest a better module?

No.