If it's fake wood veneer, there's not a great deal you can do I'm afraid…other than try and source some veneer and re-cover the table with that. Nice real wood veneer from people like here (iron on)
If it's real wood (you should be able to tell), it would have to be sanded back with an orbital, but only as long as the sanding wouldn't actually go through the veneer anyway. I reckon the iron-on option might be the best – and make sure you have a nice sharp craft knife to trim the edges, or a specific veneer trimmer – which as far as I know, aren't really that expensive. Then, apply a few coats of varnish and hey-presto, a nice new table.