The documentation states that the items that get added to an HList are DItem's. If the DItem is of the appropiate type (e.g. text and imagetext), you can apply an ItemStyle, the attributes of which include background color.

See the manpage of Tk::DItem for details. Then see the Tk::HList manpage for an explanation of how to create custom DItems and add them to an HList.

############################################################## 
sub select_color{

my $dialogcol = $mw->Toplevel(-bg=>'steelblue');
$dialogcol->overrideredirect(1);
$dialogcol->geometry('+100+100');
$dialogcol->configure(-cursor => 'top_left_arrow');

my @colors = qw(DarkGrey orange pink hotpink red
                peru goldenrod tan gold wheat
                lightyellow yellow khaki lightgreen green
                lightsteelblue turquoise cyan violet plum
                bisque beige snow);

my ($r,$c)=(0,0);
foreach my $color(@colors){
  $dialogcol->Button( -text =>$color,
              -bg=> $color,
              -width=> 12,
              -activebackground=>$color,
               -command => [\&change_col,$color],
                      )->grid(-column => $c, -row => $r);
$c++;
if($c % 5 == 0){$r++;$c = 0};
}

$dialogcol->Button( -text => 'Finished',
              -bg=>'red',
              -activebackground=>'plum',
              -command => sub{$dialogcol->destroy;
                              })->grid(-column=>$c, -row=> $r+1);


sub change_col{
      $info{$key_sel}{'color'} = shift;
      $colorbut->configure(-bg=> $info{$key_sel}{'color'});
               my $textstyle  = $h->ItemStyle('text',
                                -justify => 'center',
                                    -bg => $info{$key_sel}{'color'},
                                    -selectforeground => 'green',
                                   );
     $h->itemConfigure($h->info('selection'), 1,'-style'=>$textstyle);
  }
}
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