It doesn't look that bad to begin with. It will give you something to joke about when you sign up for a dive.
On the other hand, your instructor is right. No one has seen my OW card in nearly 20 years. I got my AOW a couple months after the OW, and it has been stashed away ever since. I am by no means suggesting that you take additional training for the purpose of getting rid of the picture, but if "the rest of your diving career" is going to last long enough to make this an issue for you, then you will be taking additional classes anyway.