Of all the finishes in the world that has to be the simplest to repair but if you must ask how,don't try it,just hire a pro. I liken this to the fact that although the Cessna 172 and Piper Warrior are the simplest planes in the world to fly,you shouldn't buy one and strick out without training after asking for tips on the net. .

if it's really finished with nitrocellulose lacquer there are going to be many more scratches joining the ones there as you use the table. I'd plan on getting used to them. If you refinish I'd get a pro to do it with a conversion lacquer, or a much tougher varnish that will be more scratch resistant

I agree with rwiegand, laquer will wind up with more scratches for a tabletop that gets regular use. This comes from my experience.

However, it sounds like you have a high-end table, so perhaps lacquer is appropriate. Is this a period dining table? And, yes, lacquer is easy to repair with fine sandpaper (grit dependent on scratch depth), perhaps 1200 grit and polish. 3M swirl remover would probably work for what you are describing.

Pre-catalyzed lacquer offers the same clarity as nitrocellulose lacquer, but more durable. You want to seek a professional if you want to refinish with something like this. Varnishes (post-catalyzed, polyurethane, etc.) are also durable, but are meant more like floor finishes, or a bar finish. I personally don't consider them appropriate for "fine furniture."

I would just polish and move on.

Good Luck.

As a repair technician who has done lots of these for pieces sitting in the store (and getting constantly "re-staged" by the decorators there), I'd have to agree with Klem. Easy for someone with the right knowledge and materials.