you can embed the widgets enclosed by the green line in an extra frame and add padding to that frame like so:

use warnings;
use strict;

use Tk;
my $mw =MainWindow ->new;
my $f = $mw->Frame()->pack(-ipadx => 5);
$f -> Button(-width => 10)->grid(-row => 0, -column => 0, -padx => 5);
$f -> Button(-width => 10)->grid(-row => 0, -column => 1, -padx => 5);
MainLoop;
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Also, your screen layout looks like it could be easier defined using the Tk::pack geometry manager.