Depends on how much work you want to put into it.
Of course it is difficult to tell just what has to be done without seeing
the problem but off hand the biggest problem could be matching the grain
since the grain of the layer under the veneer will probably run cross grain
to that of the veneer.
In any case, if your willing and have the time to do some experimenting you
can spray the offending area with some lacquer. For this type of thing I'd
use Deft in a spray can. Lowes, HD, Ace Hardware. Get a couple of thin coats
Now, see if you can find some oil paint that matches the grain color of the
veneer and get a couple of artist brushes. Also, if you are lucky you will
find a spray can of Min Wax stain and wood sealer with a color reasonably
close to that of the of the base color veneer. If not you'll have to make up
a wash of a suitable stain and finish.
Assuming you actually did find a spray can of the Min Wax with the proper
color apply light coats to the spot, feathering it towards the edges. It is
important it is the Min Wax Stain and Wood sealer. That contains a fixer
that will hold the stain in place. If you screw it up, just wipe the stain
off before it sets and try again. When you get it right let it dry.
Now, using a thin brush paint on some grain lines then feather them out to a
natural look with a wide dry brush.
Then again you could just paint it.
As an aside, using a card or cabinet scraper would have lessened your chance
of going through the veneer to start with.
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