I recently applied for a national scholarship at my university. My application was accepted internally as one of few to be sent to the organization hosting the scholarship. However, the people screening applications at my university were slightly concerned about one of my reference letters from my last advisor, and sent it to me to show me what he wrote (I'm pretty sure those letters are supposed to be confidential, but that's beside the point). A brief summary of the letter is that I'm only slightly above average, and 1/4 of the letter is about his previous research accomplishments. I can't change referees since my application has already been screened. My question is, can I ask my previous advisor to improve his letter of recommendation?
You can certainly ask, and might be successful, or not. It is impossible to say. But a better approach might be for the scholarship people to ask the professor for a better letter on your behalf, explaining the reasoning and perhaps the fact that his is an outlier.
Having an advocate may be more effective in a situation like this. Another professor might also prevail upon your advisor, but it would be impossible to hide the fact that you'd seen the letter.
(I'm pretty sure those letters are supposed to be confidential, but that's beside the point). ...
Actually, it is not. You may have signed a waiver when you applied for the position. If so, you have absolutely no recourse to ask for anything. If so, the person who sent the recommendation to you may be in violation of privacy guidelines that were been established for your previous advisor as part of his/her submission process.
When I would be the advisor whose letter was submitted under a waiver of right to see by the student and I discovered that letter had been disclosed back to the student, I would be raising holy heck to the Chair of the Committee if not the Chair of the Department if not further up the chain.
As noted, your first call was to refuse to review the letter until you had the "pretty clear" part clarified beyond a reasonable doubt. Until such a time, you best not be asking anyone anything about changing the letter.