I think this should work for you (WARNING: I did it really quickly):

#!/usr/bin/perl -w
use strict;

while (<DATA>) {
    s/^\/[\S]+\s//;
    print "$_\n";
}



__DATA__
INVALID ORDER-NO 4546090
INVALID ORDER-NO 4546090
INVALID ORDER-NO 4546090
INVALID ORDER-NO 4546090
INVALID ORDER-NO 4546090
/base-dir/dir/foo.txt INVALID ORDER-NO 4546090
INVALID ORDER-NO 4546090
INVALID ORDER-NO 4546090
[download]

This assumes your error msg will never start with /.

UPDATE: I knew I did this too fast:

I had a useless character class

didn't chomp THX tadman

so rewritten:

while (<DATA>) {
    chomp;
    s/^\/\S+\s//;
    print "$_\n";
}
[download]

grep

grep> grep clue /home/users/*