Depends on your career aspirations, or how you want to be viewed in the event of downsizing.
I remember talking to someone once about a particular measurement that we were evaluated on. This was a good worker and a smart person that thought this particular measurement was silly and the tracking was a waste of time. While I didn't disagree with the sentiment, I told them that it's a tangible thing that they can point to. You have to play along. They easily could have met the metric if they wanted to. This person was eliminated when reductions came through, largely due to that measurement.
If this person doesn't care if they are the first to go in the event of staff reductions, then stand their ground and stick with no response on "my time". If they value their job, and want to viewed favorably, take two seconds and respond that they had plans for the day and can't change them. This assumes that the text was received and deliberately ignored.