Instead of testing for the directory existance, just add error checking to your chdir.

Additionally, your opendir error check will never be utilized because you used || instead of or.

I'd also recommend that you use a lexical directory handle instead of a glob.

chdir $directory or die "Can't cd to $directory: $!";
opendir my $dh, '.' or die "Can't open $directory: $!";

while (my $file = readdir $dh) {
    print "$file\n";
}

closedir $dh;
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Within your loop, are you trying to match files that begin with the literal $filemask? If so, then you'll want to escape that using quotemeta or \Q...\E.

And as ww pointed out, I don't think you need the bareword chomp.

Don't know what $Mode is about...

    if ( $file =~ /^\Q$filemask\E/i )  {
        push @chk_files, $file;
        print "\n\t$file ";
    } # End of IF
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And finally, be sure to have use strict and use warnings turned on.