#!/usr/bin/perl --
use strict;
use warnings;
use Tk;
my $mw = tkinit;
my $Section_tblw = $mw->Table(
...
20 lines or less
MainLoop;
[download]

If you can get it down to 20 lines + boilerplate, we might make some progress

Here's your standalone:
UPDATE: using choroba's solution in Table constructor, doesn't change the issue.
Read more... (7 kB)

You seem to not define the number of rows for the table, so it defaults to 10. If you call clear, only the first 10 lines are deleted. Add

-rows => 100
[download]

to the table constructor parameters and everything works.

BTW, you can chomp @vals and push @rows, \@vals.

لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

:) Ignoring all the issues with your code with short-circuit

sub section_del {
    return $Section_tblw->clear;
[download]

looks like Tk::Table is not deleting checkboxes

so I replace that with  return my_clear( $Section_tblw ); and one or three dd-Dumper-ings later, its an off-by-one error in clear

sub my_clear {
    my $self = shift;
    my $rows = $self->cget( -rows );
    my $cols = $self->cget( -columns );
## 1st row is labels
    foreach my $r ( 1 .. $rows ) {
#~         foreach my $c ( 1 .. $cols ) {
## 1st column is 1st column
        foreach my $c ( 0 .. $cols ) {
            my $old = $self->get( $r, $c );
            next unless $old;
            $self->LostSlave( $old );
            $old->destroy;
        }
    }
    $self->_init;
    $self->QueueLayout( Tk::Table::_SlaveSize() );
} ## end sub my_clear
[download]

I imagine the OBO error migt stem because at one point the first column in each row might have been a counter (nth row) ...