So what happens if you use a Deterministic Password Generator and there is a security breach in one of the websites that you use and the password is leaked? Can

So what happens if you use a Deterministic Password Generator and there is a security breach in one of the websites that you use and the password is leaked? Can you generate a new password for that website? If this requires adding a parameter to password generator, like --iter 2 for example, how do you remember the parameter for each website?