That's easily done with substitution:

$string =~ s/\\'\\'//;
[download]

Or more elegantly...

$string =~ s/\Q\'\'\E//;
[download]

...where \Q and \E eliminate the need to escape the backslashes. Actually, for such a small substring, \Q and \E may just look like too much line noise.

This will remove the first occurrence. If there are multiple, you have to modify with /g.