Use parens instead of curly braces when defining a hash

my %H1 = (
        'THINGS' => ['thing1', 'thing2'],
        'PEOPLE' => ['andy', 'margot', 'dave', 'joe'],
);
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Thanks ccn. Now if I wanted to delete 'dave' I could do ...

delete @{$H1{'PEOPLE'}}[2];
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... but that leaves my hash looking like this ...

$VAR1 = 'PEOPLE';
$VAR2 = [
          'andy',
          'margot',
          undef,
          'joe'
        ];
$VAR3 = 'THINGS';
$VAR4 = [
          'thing1',
          'thing2'
        ];
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How can I free up that 'undef' array element ? Thanks

use splice instead of delete for array elements

Side note... consider passing a reference to a hash to Data::Dumper:

print Dumper(\%H1);
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{ ... } creates a hash initializes it with the contents of the braces, and returns a reference to the hash. It makes no sense to assign that to a hash variable.

When you use parens instead of curlies, it builds a list. When a list is assigned to a hash variable, it's treated as a sequence of key-value pairs. In the code you presented, there's only one value in the list (a reference to a hash), so it's treated as a key after issuing a warning.

That explains the problem you were already told about. You have a second problem, though.
grep($thing, @{...})
means
grep { $thing } @{...}
Since $thing has a true value, that's the same as just
@{...}
You probably want to use
grep($_ eq $thing, ...)

use strict;
use warnings;

my %H1 = (
        'THINGS' => ['thing1', 'thing2'],
        'PEOPLE' => ['andy', 'margot', 'dave', 'joe'],
);
my $thing = 'thing1';

if (grep {$_ eq $thing} @{$H1{'THINGS'}}) {
    print "found\n";
}
else {
    print "not found\n";
}
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Not using strictures (use strict; use warnings; - see The strictures, according to Seuss).

Using warnings would tell you "Reference found where even-sized list expected at ...".