somehow, you ended up posting your question on *** ****s web site as a reply to someone elses question rather than a new question of your own.
So, removal of the caulk damaged caused damage to the drywall? What is the damage like and how did it happen? Did whatever your husband was using to remove the caulking cause the damge or did simply peeling up the caulking cause the damge? Did the removal take off the paper layer on the top of the drywall or did it just peel off the paint and texture (if the paper layer is gone, you will be looking at a chalky substance in the damaged area rather than paper). Is there a divot or just paper ripped off?
What kind of a backsplash are you talking about? Is it a formica couter backsplash or a backsplash of some other material?
You know, I am a little concerned because if the drywall was damaged when you removed the caulking and the backsplash is warped... it may be that you have water damage that is to blame for the warpage and the damaged drywall. Without seeing it, I couldn't tell you. You will have to look and see if you can find signes of water damage.
So, you can cover up the damage (tell me a little more about what the damaged drywall is like and I will see if I can help).
HOWEVER, IF there is water damage that is causing these issues, you need to find the source of the water damage to ensure that continued damage does not occur. Then depending on the extent of the damage, you can decide whether to cover it up or replace materials.