Well, pg's solution works for the limited input provided and you haven't given any further particulars regarding input. That solution breaks just changing the first word from "thought" to "though" :

my $var = "though test tot 1 2 3 tesset";
$var =~ s/(t.*?t)/($1 ne "test") ? "" : $1/ge;
print $var;  # prints: esoesset
[download]

But, now you mention a further constraint that the words to be deleted may not contain any 't's inside, which is not inferrable from your earlier posts at all. Providing a good specification is much more than providing a sample case (but providing test cases *is* important).

Anyway, here's a go at your new specs:

my $var = <<TT;
target blah foo test thought 123 though tempest
testament though tightest treatment thermostat tantamount taboo
TT
$var =~ s/(?!\btest\b)(\bt[^t\W]*t\b)//g;
print $var;
__END__
## Result:
 blah foo test  123 though 
testament though tightest treatment thermostat tantamount taboo
[download]

So, all the 't.*t' words on the second line remain because they contain a 't' character within. All the 't.*t' words on the first line get deleted except for 'test'.