Thanks. I was really hoping to find a setting to turn this off, but I
was at least able to do an Advanced Find on the calendar for
"birthday", select all items, right-click and choose Open Items, and
then manually set each one to be no reminder. I will have to remember
that if I add a birthday to a contact in future, then I will have to
remember to remove the reminder, and I will have to do that manually.
It seems like a real oversight in Outlook, but at least I have sorted
this out.

Thanks for your advice