Screws, while essential, aren't aesthetically pleasing, and they can diminish the look of vintage hardware. Fortunately, ...

Use a hand-held belt sander with 80-grit sandpaper to level off the brass screw head so it’s even with the surrounding wood. Brass is soft, so leveling happens easily. Just be careful of heat.

Mix sawdust from the table wood with wood glue to create a thick paste. ... but repeatedly removing and replacing the hinges is probably going to damage the brass screws, screw holes, or both.