A simple fix would be to do a few checks before you make the substitution:

use strict;
use warnings;
use Data::Dumper qw{Dumper};

my %hash = (
        'GREETING1'    => 'HAI',
        'GREETING2'  => 'HELLO',
);

              
my $value = '-GREETING1- James -POSITION- -GREETING2- -FOO-';

## find potential matches
my @matches = $value =~ m/-([^\-\s]+)-/g;

## give summary
print "" . (scalar@matches) . " matches for >>$value<<:\n" . (Dumper \
+@matches);

## check each potential match before substituting
for my $match (@matches){
    if (exists$hash{$match}){ # recognised?
        ## make substitution, including updates on string
        print "\t>$match< replaced:\n";
        print "\tWAS : $value\n";
        $value =~s/-$match-/$hash{$match}/;
        print "\tNOW : $value\n";
    }
    else { print "$match not replaced.\n"; }
}
[download]

Gives:

4 matches for >>-GREETING1- James -POSITION- -GREETING2- -FOO-<<:
$VAR1 = [
          'GREETING1',
          'POSITION',
          'GREETING2',
          'FOO'
        ];
    >GREETING1< replaced:
    WAS : -GREETING1- James -POSITION- -GREETING2- -FOO-
    NOW : HAI James -POSITION- -GREETING2- -FOO-
POSITION not replaced.
    >GREETING2< replaced:
    WAS : HAI James -POSITION- -GREETING2- -FOO-
    NOW : HAI James -POSITION- HELLO -FOO-
FOO not replaced.
[download]

Not a one liner, but maybe a bit clearer to follow and easier to expand later... HTH!

Updated: Added some comments...