It doesn't. Pets count as their own entity with their own buff table.
Warrior shouts apply to all party members within range. Greater blessings only apply to the specific class and treat pets as a class for the purposes of receiving the buff. If you GBoK one warlock pet, it applies to all warlock pets even if you have different pets summoned.
I don't have a hunter so I can't test whether the same is true between warlock and hunter pets.
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