Wood replacement is the typical and easiest method used by shops looking at this type of repair. It's harder, to repair the piece, but often, particularly in a restoration
the only way to go.
The image shows damaged veneer and possibly some solid wood. It looks like something repeatedly rubbed against the area, right through the finish.
This finish can't be "touched" up in the usual sense, but the area can be restored to a large degree. If the patina is desired then scrape the finish from the surrounding areas, until the varnish is all dull. Very lightly feather the damaged area back into the good spots with 180 grit, progressively moving through 280 grit (always with the grain). This will soften the damage edges and semi smooth the rubbed areas. Next carefully apply a mixture of 70% varnish, 30% spirits to the raw wood only. Do this once and let dry. If the raw wood looks very dull, do it again. It it has a slight sheen (it probably will) then use straight varnish for the next two coats.
Now you have damaged wood that is sealed and abutting scrapped varnish. When the varnish is good and dry (at least 24 hours), knock down both areas with 220 grit, again working to 280 or 320 with the grain to blend the newly sealed damaged areas with the surrounding varnish. You can start revarnishing the whole piece as if nothing happened. It will show some of the distress
and patina, but the surfaces will be blended and the damage much less obvious.
If you want to remove the damage completely, then the pieces need to come out, the whole of the finishes scraped off, the damage bleached and other wise "treated" to hide and remove the stains and imperfections.
Working veneers is a delicate process as you might imagine. You only have so much room to work with (the thickness of a veneer). The damage above looks like it could be easily fixed, with a slight patina showing, but shinny and varnished, which most don't find objectionable. To fully remove the damage, you'll have to do considerably more and replacement then becomes a viable option. As far as cleaning
the surface, you'll get the mold
(very little showing) with a diluted bleach and water
mixture, but the wood has moisture damage which will have to be treated. There are a few ways to handle this, but most will still leave a slight discoloration, which under varnish becomes a wear patina.
A quick way to see how things will look with the wear patina is to wet out a rag with spirits then wipe the damaged areas with the rag. This will give you a good idea of the color changes that will take place with new varnish over the damage. Naturally, it'll look much better under varnish, then a quick wipe of spirits, especially if you're diligent about the blending and smoothing process, but this is an easy way to get a look at the end result before you do anything. The spirits will eventually "flash off" (evaporate) and you'll have raw, damaged wood again.