Can a stain be removed from a composite resin veneer without damaging the tooth and enamel underneath? (Photo)

The only way to really remove a permanent on a resin veneer is to redo the resin veneer.  This should not damage the underlying tooth or neighboring teeth.  Unfortunately, resin veneers are prone to staining, so this is why I recommend porcelain veneers because they are so permanently white, like your toilet bowl. I hope this helps,Dr. Sarah Thompson

The stain in your dental bonding, needs to be repaired! Your good dentist can remove the stain by polishing and if it is deep, or there was a porosity, your dentist can easily add to your composite material with new composite. This will not cause any damage to your enamel. The composite bonding can be repaired.

This should not be that difficult to correct.  Call and schedule with your dentist to correct this when you are able to.   

Composite veneers as on your teeth are the same material that white composite fillings are made from. 
This means they come out of a syringe or cartridge, but they inherently have tiny air bubbles whilst they are in their container. When they are applied to the tooth the air bubbles can appear solid but are really quite weak. After the slightest impact the bubbles burst and let staining settle in them.
If they are small areas, a repair after cutting back some of the matter is quite straightforward. If the areas are larger, the same technique can effectively mean that the veneer is redone.
It is your dentist's responsibility to correct this so simply speak to him or her and it will be corrected for you.
Kind regards
Thomas Dey, BDS, MSc

Looks like an easy fix!  Appears to be some small voids in the composite material and can be cleaned off and rebonded and polished smooth.  This is the beauty of composite veneers but durability and discoloration of years is what you may give up.I would also suggest avoiding sodas and acidic drinks as these may roughen the veneers over time and allow stain to start appearing.

This should be able to be repaired quickly and easily and most often without any local anesthesia. There was probably a small void or air pocket in the original composite that caused this.  Should not damage the tooth structure at all.

Hi:
It is difficult to tell the depth of the stain.  However, generally  this can be done without any damage to the enamel of the tooth.
Best,
Dr. Maddahi

It is possible the discoloration is from "bubbles" or pockets of air within the composite material itself, and only total replacement will fix this.  Minimal to zero damage to the tooth is possible, but the minor discoloration is just that.  Minor.  The veneer is not weaker or compromised, and only you and your dentist can even see this spot.