Under Unix/Linux, you can try using Net::OpenSSH that's more perlish:

use Net::OpenSSH;
my $ssh = Net::OpenSSH->new(...);

my $out_fh = $ssh->pipe_out("egrep -l $searchStr * 2>&1 | tee ~/myfile
+.txt\n");
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Then, the returned $out_fh object will be a real and fully working file handle that can be used, for instance, inside a non-blocking select loop.