They have a lot of power and influence. If the Iron Throne were to screw them over they would almost certainly impose some sort of embargo, thus crippling their economy. They are quite rich too and would defeat them by funding their enemies and/or hiring their own army of sellswords etc.
I'm sure there are limits to their power and they could theoretically be defeated, but for the purposes of the show I think it is best to assume they are pretty much invincible and can endlessly bankroll the fight against people/countries that don't pay up.
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