Assuming you don't have a huge list of files to delete, this should be a reasonable approach. A couple of things...avoid system and backtick calls if you can do it easily within.

#!/usr/bin/perl -w

use strict;

my $del_dir = "/directory/location/of/files";
my $del_days = 7; #delete files that are X days old
my $now = time();
my $del_date = $now - (86400 * $del_days); #current date - (second per
+ day * days)
my @dir_list;

chdir $del_dir;
opendir(DH, $del_dir) or die "Unable to read $del_dir directory.  ERRO
+R: $!\n";
@dir_list = grep { /(txt)$/ } readdir(DH); #build list of files that m
+atch "txt" extension
closedir(DH);
foreach (@dir_list) {
    my ($file_time) = (stat($_)) [9];
#    unlink $_ if ($del_date > $file_time);
    print "If the above was not commented out, $_ would have been dele
+ted!\n";
}
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-THRAK