If there is a certain amount of grief mixed in with the Compassion, then I suggest that you can note this. If however there is a sense of being "touched", a sense of being awed by the amount of Dukkha in the world, then I don't suggest that we note so much the changes in the face at that time, because this may be helpful for us to motivate that compassionate intention, opening to Dukkha.
If however there is a sense of grief arising, and a sense of pulling back from it, then it may be helpful to actually note this and see how the resistance to opening to Dukkha is affecting us and bring up some Compassion for ourselves at that time. It is quiet a challenge sometimes to keep our Compassion balanced. So, if we do see a tendency to go into grief, it is important for us to see this arising in ourselves. And it may be helpful later to balance such a tendency with reflecting more on the third and fourth Noble Truths so that we strengthen our sense of refuge. By strengthening our sense of refuge we may be able to find more courage to open progressively and gradually more to the existence of Dukkha without getting upset that it does exist.
This again is an interesting question and it could be helpful for the person who wrote it to bring it up in the interview so we see actually what is arising for you and what may be necessary to balance such a tendency. It really depends on what else is going on there to give a more "complete," correct answer, for this person.