In almost all the Perl solutions posted so far, there is the common denominator while (/.\x08/). I don't like it because it scans again some parts of the string that already have been cleaned up. So I've worked out something using m/\G.../g, that continues scanning where it left off:

my $text="ABC\x08\x08\x08\x08\x08DEFGHIJKL\x08\x08M\x08NOP\x08\x08\x08
+\x08\x08\x08\x08QRST";
while ($text =~ /\G.*?(\x08+)/g) {
  my $c2r = 2 * length $1;       ## number of chars to remove
  my $st  = (pos $text) - $c2r;  ## start
  $st++, $c2r-- while $st < 0;   ## maybe there are too many \x08's ne
+ar the beginning
  substr $text, $st, $c2r, '';   ## wipe erased characters as long as 
+their corresponding \x08's
  pos $text = $st;               ## make \G resume in a sensible place
}
print "$text\n";
__END__
DEFQRST
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