Y need to use the option -relief => "flat" and it will show as not having any line between adjacent values,as in the following example

#!/usr/bin/perl
use warnings;
use strict;
use Tk;
use Tk::Table;

#The key point is that the scroll bars only scroll non-fixed columns.

my $mw = MainWindow->new;
#$mw->geometry("200x200");

my $x;
my $y;

my $table = $mw->Table
  (-rows => 9, -columns => 9, -fixedrows => 9)->pack;

  foreach my $row (0 .. 8) {
      foreach my $col (0 .. 8) {
          my $cell = $table->Entry (-width => 4, -text => "$col, $row"
+, -relief => "flat");
                      $table->put ($row, $col, $cell);

      $cell->bind('<ButtonPress-1>' => sub{ $x = $col; $y = $row  });
  }

}

my $button = $mw->Button(-text => 'Get Current',
                -command => sub{
                     print "$x $y\n";
                })->pack();

MainLoop;
__END__
[download]

Thank you! It works perfectly!