But Mr and Mrs Green are not the ones paying for the employees' health care. Rather, those checks are from the corporation.
No, they are a privately held corporation. They are taxed on the companies total net income just like they were a partnership. As such, if paying for the IUDs and morning after pill costs the company, it costs them directly. It was specifically because of this direct pass through of income and its treatment by the IRS that the courts found in favor of Hobby Lobby. If Hobby Lobby were a publicly traded corporation, they would have lost the case, because only dividends are passed through so it is just an investment and they could chose to invest in other companies. But that is not the case.
Maybe you don't understand how employer health care works. The reason an employer provides health care is because an employee works for them. So, in a very real way, the value of the health care has already been earned by the employee. Thus, it's not Mr and Mrs Green paying for the health care at all is it? It's the employees who pay for it, with their labor (and also direct deductions from their paychecks). Employer health care is not charity.
I understand exactly how employer health care works as I am responsible for it of our organization. However, the Hobby Lobby case is not about employer health care, it is about the HHS mandate of the affordable care act. Now, it is possible that the Greens don't subsidize any of their employee's health care and the employee pays 100% of the cost. It is possible, but very unlikely.
I do agree that employee health care is not charity, it is part of the benefits provided to workers, since WWII. This isn't about health care. It is about the government saying that the Greens must pay for something that is contrary to their religious belief. The belief in question is that they believe that life begins at conception and making them pay for IUDs means they are being forced to pay for abortions. We may not agree with their belief, but that doesn't matter. The government cannot force somebody to violate their religious beliefs, even if it is for the common good, if the government can achieve the goal through other means that don't violate the persons religious belief.