Are there any restrictions on buying a plane ticket to the United States with a green card?

Obviously, that man is talking nonsense. You have a green card to enter and leave the country directly through the permanent resident channel, without looking at the ticket.

Of course, some airlines may offer some preferential air tickets, and do not rule out similar conditions such as requiring new immigrants. But this is a company behavior, and it has nothing to do with immigration.

Rest assured.