Bondo to the Rescue
In order to repair veneer damage we often use bondo. It isn't porous so when you paint over it after sanding it doesn't look like there is a repair...just nice and smooth!
Bondo comes in two parts that you need to mix together.
The directions aren't exactly what works in reality...at least not for me. You want to mix it in so its like a greyish maroon color. My super professional measuring is like this.....a tablespoonish of the grey stuff and about 3/4" to an inch of the red stuff.
Apply it to your damage....
We use a putty knife but be sure all your loose veneer is removed first!
Sand once it has dried and you are ready for paint! ALL better! You can also use this to recarve missing appliques, etc. Its a miracle!