My add-in card uses a pair of pins to drive an external activity LED, with anode "provid[ing] 220 ohm pull-up to +3.3 V".
However, the LED that I wish to drive with these pins, is designed to be driven by "LED pull-up to +5 V".
How do I proceed?
What they're saying is the '5V LED' has internal resistor. Your card also has a resistor (220 ohms). So what will happen is that the LED will be very dim since it will be running on 3.3V -> 220 ohm -> LED dropping resistor in series.
If you can modify the LED to short out the resistor it could work, or replace it with a plain (non-resistor) LED.