Every team experiences this at one time or another. The correct answer is:
When we finish the sprint backlog, if there's time, that item will be the next one the team attempts.Do not let management, or anyone else, influence what you accept into the sprint backlog. This is the team's commitment to itself.
The answer above must be automatic with no delay. Delay is a sign of weakness the clever manager or stakeholder will seize upon. The do not understand the implications of adding extra work to the sprint backlog but you do.
We know that too much work-in-progress (WIP) is a productivity killer.
Accepting more work than you can commit to in a sprint undermines a primary purpose of doing sprints. The team is making a commitment to the items in the backlog. They will be done during the sprint. [There are legitimate reasons that an activity should span sprints. The part to be attempted and to which you are committing to during a sprint should still be clear.]
Undermining the commitment process has a long term effect. The team quits thinking of the sprint backlog as their commitment and just a list that fits the velocity. They quit reaching.
When you accept extra items in the sprint backlog are you committing to them or acquiescing to the stakeholder? "When we finish the items we are committing to we will attempt to work on the item you want in the sprint." Period.