If it’s black black I usually use a sharpie but your other options are either look for a marker in that color (if possible) or buff them out and repaint the door, then try a glossy top coat to prevent this problem going forward...

This is Tricorn Black which is a pretty true black.

Did you find something that works? I also have Tricorn black doors, and my small dogs have done the same thing!

Repaint, that is to much in the way of scratches to "touch up".