This is a hack, but seems to work on linux. I noted 2 needed (but weird) focus calls, that I found by experimenting. :-)

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

my $mw = new MainWindow;

my $warning = 'alphanumeric entered';
   
my $tl = $mw->Toplevel();             
$tl->geometry('300x100+300+300');                                     
+       
my $wlabel= $tl->Label(-textvariable => \$warning)
     ->pack(-expand=>1,-fill=>'both');
$tl->withdraw;

my $new_label = $mw -> Label(-text=>"Enter any character",
    -foreground=>"red",
)-> pack(-side=>"top");

my $ent=$mw->Entry()->pack();

my $press = $mw -> Button(-text=>"Show Me",
       -command =>\&PressMe,
          )-> pack(-side=>"left",-padx=>"5", -ipadx=>"5");


$mw->bind( '<FocusOut>' => sub{ 
            $tl->withdraw; 
            $mw->focus;  #hack needed to prevent recursion
            } );

$mw->bind( '<FocusIn>' => \&PressMe );

MainLoop;

sub PressMe{
    my $val = $ent->get();

 if ($val =~ m/[a-zA-Z0-9]/) {
      $tl->deiconify; 
      $tl->raise; 
      $ent->focus;   #hack needed to prevent recursion
     }
    return;
}
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