use GreekFile qw/gr_glob gr_open/;

binmode STDERR, ":utf8";  # might help for error reporting

# ...

my @files = gr_glob( "../data/text/*.txt" ); # @files is an array of utf8 strings
  # because the gr_glob function in GreekFile.pm handles that conversion

my %display_files;  # let's store file names in a hash
for ( @files ) {
    my $f = $_;
    $f =~ s/\.txt//;
    $display_files{$f} = $_;  # use hash keys for display, hash values as file paths
}

# ...

my $passage = param( 'select' ) || "blah blah (in Greek)";
  # $passage is assumed to be in utf8

if ( exists( $display_files{$passage} ))
{
    gr_open( FILE, "<:utf8", $display_files{$passage} )
        or die "$0: $display_files{$passage}: $!";
    local $/;
    my $data = <FILE>;  # $data is assumed to be utf8

    # ... do stuff with $data ...
}