I've never seen anything indicating that the Confederates at Andersonville sent a letter, but there are two incidents involving prisoners that come pretty close.
There was a party of six prisoners released in August, 1864 to bring a petition to Lincoln asking for supplies to be sent to the prisoners and for a resumption of prisoner exchanges. Lincoln declined to release with them. One of the six, Edward Wellington Bates, wrote about the incident for one of the Confederate Veteran's magazines after the War. The six were: Boate of the 42 NY; Henry Higginson 19 Illinois; Prescott Tracy, 82 NY: Sylvester Noirot or Norrit, 5th NJ; and William N Johnson and F. Garland, no regiment given.
Interestingly, Bates was the court reporter at the Raiders' Trial and Higgins was supposedly the raiders' defense attorney (although he was actually an insurance salesman).
Lincoln declined to meet with the delegation, to Boate's fury. The six did not return to Andersonville.
There was also a letter that circulated in several newspapers late in the war, which read:
At a mass meeting held September 28th, 1864, by the Federal prisoners confined at Savannah, Ga, it was unanimously decided that the following resolutions be sent tot he President of the United States, in hope that he might take such steps as in his wisdom he may think necessary for our speedy exchange or parole." It was signed P. Bradley. This passage is from John McElroy's book, and while McElroy was definitely a POW at Andersonville, he twists things so much that I do not consider him to be a reliable source.
This may be the letter you're thinking of. Since some of the Andersonville prisoners went home by way of Savannah, this may or may not have been from Andersonville prisoners.
John McElroy assigns this letter to Pete Bradley, who he claims was a NYC "shyster" who represented the raiders at their trial. Problem is, there's no record of a prisoner named Peter Bradley ever being held at Andersonville, and no record of anyone by that name ever practicing law in the state of NY between 1860 and 1865 (Trust me, I went through the names of every lawyer in the state at that point in time while researching my book on the raiders). There was Patrick Bradley, 2nd Mass Heavy Artillery, but there's no proof that he penned the petition, either.
I'll have to go dig for the primary sources, but it may take a bit. The superintendent has decided that I'm one of the teachers going back into the school building tomorrow, even though there were 200 new cases of covid last week, so when I'm not prepping, I'm stressing.