Marble countertops are among the most valued and expensive kitchen surfaces. It's a natural stone, and as such is porous and requires sealing to make it suitable for use as a kitchen surface. One of the problems with this kind of natural stone countertops is that it can get scratched. Luckily, there are many products to use to get scratches out of marble.
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You can remove small superficial scratches using a product known as marble polish, available from most DIY stores under a variety of brands. Look for products labeled marble polish or marble repair kits in a color similar to your marble countertops. Those products are non-abrasive and will fill the small scratches and allow you to buff the marble surface to make it as glossy as new.
Start with sanding the marble very gently using a fine-grained sandpaper. To avoid making problems worse, make sure you do this very, very carefully, as your goal is to make the scratches more even, not make a worse one. Once done, mix the marble polish with water (if it's a powder) until it has the right consistency, and apply it to the scratched area. Use a clean, soft cloth to buff to marble to a brilliant shine.
Most commercial products to use to get scratches out of marble won't work with deep scratches, especially those that have gone through the dressing and affected the marble itself.
To fix those you will need to remove all the dressing from your marble countertop, by sanding it slowly using a dry sandpaper or dressing stripper. Then you will need to sand out the scratches on the marble surface itself, and most importantly, reapply the dressing to the marble countertops to seal them and protect them from the elements.