Rather than reading the data line by line you could slurp all of it into a single scalar string then split into per-team chunks at each point in the string that is followed by a "T" at the start of a line. Then for each team get rid of the [PT]: characters globally and split again on newlines into the team line and player lines. This gets rid of the need to test each line for a "T" looking for a new team. Finally, as hippo suggests, de-dup before building your HoA;

use 5.026;
use warnings;

use Data::Dumper;

open my $dataFH, q{<}, \ <<__EOD__ or die $!;
T:REDS
P:GRIFFEY
P:GRIFFEY
P:PEREZ
P:GRIFFEY
P:PEREZ
P:ROSE
P:BENCH
T:PHILLIES
P:ROSE
P:ROSE
T:MARINERS
P:GRIFFEY
P:PEREZ
__EOD__

my $data = do {
   local $/;
   <$dataFH>;
   };
close $dataFH or die $!;

my @teams = split m{(?=^T)}m, $data;
my %teamAccts;

foreach my $teamData ( @teams )
{
    $teamData =~ s{[PT]:}{}g;
    my( $teamLine, @playerLines ) = split m{\n}, $teamData;
    $teamAccts{ $teamLine } = [
       do {
          my %seen;
          grep { ! $seen{ $_ } ++ } @playerLines;
       }
       ];
}

print Data::Dumper
   ->new( [ \ %teamAccts ], [ qw{ *teamAccts } ] )
   ->Sortkeys( 1 )
   ->Dumpxs();
[download]

The output.

%teamAccts = (
               'MARINERS' => [
                               'GRIFFEY',
                               'PEREZ'
                             ],
               'PHILLIES' => [
                               'ROSE'
                             ],
               'REDS' => [
                           'GRIFFEY',
                           'PEREZ',
                           'ROSE',
                           'BENCH'
                         ]
             );
[download]

I hope this is of interest.

Update: Clarified wording slightly.