kennethk has provided a solution.

When your code doesn't work as expected, one debug technique is to use B::Deparse to see what code you are actually running (Tip #6 from the Basic debugging checklist). This shows that those angle brackets are really File::Glob:

perl -MO=Deparse 844275.pl
print "Customer abbreviation:\t \t";
$cust = <STDIN>;
print "\n";
chomp $cust;
use File::Glob ();
until ($cust =~ glob('w{3,4}')) {
    print "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n";
    print "!!!                                        !!!\n";
    print "!!! ABBREVIATION MUST BE 3 OR 4 CHARACTERS !!!\n";
    print "!!!                                        !!!\n";
    print "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n";
    print "\n";
    print "Customer abbreviation:\t \t";
    $cust = <STDIN>;
    chomp $cust;
    print "\n";
}
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