In a word - carefully.
Each grill has eight pins which push into plastic retainers. All of them have likely become very fond of each other in the last 45 years or so. 😕
I suggest looping a piece of wire under some of the slats at one far end of the grill. Do not position that wire in the middle of the slats where they are the weakest .
Next, apply sufficient protective masking tape around the grill and get a small putty knife; this is a better tool to use for prying than a screwdriver that may more easily chip paint.
Use the putty knife to gently pry at the end of the grill while you are pulling straight up with the wire.
If things go smoothly that should allow you to gently pry all eight pins loose.
If things don’t go smoothly continue the process, re-positioning the wire and putty knife as required.
Do not get frustrated and try brute force as the grills have been known to break. I believe they are just pot metal.
Good luck!
Larry