Or, you could manipulate the listbox directly using Subwidget.

use strict;
use warnings;
use Tk;
use Tk::BrowseEntry;

my $var;

my $mw    = MainWindow->new;
my $frame = $mw->Frame->pack;
my $be    = $frame->BrowseEntry( -label => "Label", -variable => \$var
+ );
$be->insert( 'end', "opt$_" ) for ( 0 .. 20 );
$be->pack( -pady => 5 );

my $lb = $be->Subwidget('slistbox');

my $bu = $frame->Button(
    -text    => 'Delete Selected',
    -command => sub {
        $be->delete( $lb->curselection ) if $lb->curselection;
        $var = '';
    },
)->pack( -pady => 5 );

MainLoop;
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