Part of the job description for GM includes other tasks as assigned. Sometimes this might mean working on inbound if that is where the business need is. We all have aspects of the job we do not like doing but we do them because it needs to be done.
Given you are a DBO (implied in another of your threads), there is a higher expectation for you. You certainly can ask about not being scheduled on inbound anymore; the worst they will say is no. But it does make it seem like you don't want to put in the work when it is needed. In your other thread it sounded like you are only filling in for the inbound TMs who are on vacation so it is not something that would happen every week.
