Bad composite resin, is removal an option? (Photo)

For all of those reading and considering composite veneers, I would strongly advise against them! You may save some money upfront, however in the long run, porcelain veneers are a much better option. 
The short answer to your question is yes, you can remove the composite, but its almost impossible to go back to your original teeth. Normally when composite veneers are placed, the dentist will roughen the surface enamel to increase the bond strength. This permanently alters your teeth.  Also, when removing composite, its extremely difficult to see where the composite ends and your tooth starts, this will also result in more tooth loss.
I would recommend seeing a expert cosmetic dentist to fix your smile.  Have them carefully remove the bulky composite and prepare your teeth for minimal prep porcelain veneers. Porcelain is a much more natural looking and feeling material. Composite veneers are made out of plastic and tend to discolor and dull over time. They are also very technique sensitive and require a very skilled dentist to make them look and fit good. 
Porcelain veneers are made in a lab and generally are placed in 2 visits. When properly done, they should last decades, whereas composite needs to be replaced every few years. 

The advantage of composite veneers is that they can be easily modified/Repaired/ Replaced. In your case, you can talk to your dentist if he can modify them to your liking or else you may need to visit another one who would be more proficient at Esthetic composites. 

Hi:You can definitely replace the composite veneer with another one that is much more aesthetic.  However, If you only want to take it off and not replace it then the amount of tooth structure that was removed to place the composite veneer plays an important role.Best,Dr. Maddahi

Anterior cosmetic restorations (like veneers) are very dependent on the eye of the dentist and how effectively the patient communicates what they are searching for as a final result.The composite veneers can be modified quite easily, thinned and de-bulked.  I would ask the dentist if they can adjust them as it should be a simple process.