I assume you mean the cabinets are painted with a high gloss paint. If that is the case I would purchase a product called Dirtex. It's available as a powder and is very inexpensive. Follow the directions on the box. I use it for walls, but it can be used on wood. I prefer it over TSP as it does not need to be rinsed off. A single step is always better in my opinion.

I would start by wiping with a micro-fiber cloth that has been dipped in warm water and wrung out. If that doesn't work, I would try a mild cleaning product. Something as simple as dishwashing liquid mixed with water could work.

Thank you! Our kitchen will be finished this weekend so the cleaning will begin!