If it has been changed after you bought the ticket you need to call the BA Contact Centre and explain that you bought the ticket expecting a BA operated flight. They have Customer Guidelines which should then allow you to shift the flight(s) before or after to avoid the Eastern service. This is the same whenever BA leases in equipment. It would not apply if Eastern was already shown in the reservation at the time of booking, and you are only supposed to have one such involuntary change, you can't keep hopping between flights.