Try using wood putty and a stain stick to match color.
You can sand veneer, Kim. Use a fine grit sandpaper and see if you can blend in the scratch. If it's deep, you can save the sawdust, mix it with some wood glue and fill it in. Once that's done, apply a new finish to the table.
Dorothy's advice is good. Filler, stain, and panel crayons make the color match easier.
I like to use auto body filler (Bondo) because the adhesion is better. It generally requires painting but it can be tinted. https://www.hometalk.com/34340531/using-and-tinting-auto-body-filler-for-wood-repair
Lightly sand to level if needed. You can use Minwax Blend Fil pencils to fill in. Then Minwax Stain marker to match. Come in all wood tones
Sorry but the pic is not clear as to what the issue is.
There are stainable wood fillers you can use if this will not sand down.
Be careful sanding veneer, it is thin and use a light hand as to not damage it more than it is.
Lightly sand then fill holes and cracks with either wood filler or bondo. Sand again. then you can paint it.