Like this?

#!/usr/bin/perl

use strict;
use warnings;
use feature qw/say/;

while(<DATA>) {
    chomp;
    s/<([0-9A-F]+)>/"<" . hex($1) . ">"/eg;
    say;
}

__DATA__
JDW-HP 1MVWV93V7j2Hxsa0Ag6 24:00:00 SUBJECT_EXACT _Did you<A0>serve ou
+r<A0>country? -New VA Home.Loan Program_
JDW-HP 1MVWV98Ddd4fLsa0Ag6 24:00:00 SUBJECT_EXACT Did.you.serve_our co
+untry? New-VA Home<A0>Loan Program_
[download]

Output:

$ perl 1095788.pl
JDW-HP 1MVWV93V7j2Hxsa0Ag6 24:00:00 SUBJECT_EXACT _Did you<160>serve o
+ur<160>country? -New VA Home.Loan Program_
JDW-HP 1MVWV98Ddd4fLsa0Ag6 24:00:00 SUBJECT_EXACT Did.you.serve_our co
+untry? New-VA Home<160>Loan Program_
$
[download]

For more on the s// (substitution) operator, see e.g. Regexp Quote Like Operators. The above substitution is fairly straightforward; it looks for angle brackets with one of more hex digits in them, and replaces them with the result of a snippet of code that gets evaluated for each match (hence the /e modifier to the regex). The /g modifier makes this a global operation so that all occurrences are given this treatment, not just the first.