I don't really care. I've gotten my flu shot on site in the past.Not sure how how you feel but even if you're vaxed I don't see that your medical history is any of their concern.
Edit: For the record, I am against the mandate, but I made my vax decision before that was a consideration. I thought long and hard about it before deciding to get it. To be honest, I think I actually had the bug last year or earlier this year (I forget). No real symptoms other than loss of taste and smell. My taste is still jacked up.