I saw a few web sites looking to not do business with from "Host Marriott", but did not see "Marriott International". From what I could see, Host Marriott is a real estate investment trust that owns many hotel properties, not all of them obviously Marriott chains (the link has a list of properties). They include Sheratons, Hyatts Hiltons, W, etc. It appears to me that this requires more precision than a blanket boycott.