Use 'under protest' to express that you're complying with something but with reluctance or resistance.

Reluctant Compliance

Conveys feelings of frustration or annoyance; not just disagreeing, but also upset about it.

Emotional Overtones

Even without openly arguing, using 'under protest' implies you don't agree with the decision.

In a legal context, indicates that actions are taken without conceding to the opposing side's arguments.

Use it to make clear that you're reserving your rights while awaiting a dispute's outcome.

It marks your action as a point of contention, indicating a dispute may follow.