You can repair the backlight, however it's a crazy difficult annoying process. You'd be better off just putting a new display assembly on there. Too bad you don't have pictures of this led Apple logo. Sounds sweet
[product|IF314-000]
Here's a link to a 6s backlight, if I don't get reported
https://www.google.com/aclk?sa=L&ai=C-zy1mbqyVqPhHIacjAa0x4XIDYn1u7AH2bbRvMcB-eSpysAECAQQAiD4mYsSKAdgybbgiZSkmBPIAQeqBCdP0LAzSUO1ylXdPwB8XVzzQW2BP7U1MG210ihtK7QkWO0O5_hV70CABZfgvAvABQWgBibYBgKAB9uAjhWQBwOoB6a-G9gHAeASxOWfwLj_9Jj5AQ&sig=AOD64_1RNacvVqvgbYwxlYXCsflT4nWQCg&ctype=5&clui=8&q=&ved=0ahUKEwiRgZ_-it3KAhVKAxoKHXDzAEsQwg8IHw&adurl=http://rover.ebay.com/rover/1/711-117182-37290-0/2%3Fmtid%3D1588%26kwid%3D1%26crlp%3D53601919689_324272%26itemid%3D252251608107%26targetid%3D154774696569%26rpc%3D0.22%26rpc_upld_id%3D62866%26device%3Dm%26mpre%3Dhttp%253A%252F%252Fwww.ebay.com%252Fulk%252Fitm%252Flike%252F252251608107%253Flpid%253D82%2526chn%253Dps%26adtype%3Dpla%26googleloc%3D9019667%26poi%3D9019654%26campaignid%3D239125209%26adgroupid%3D14978428809%26rlsatarget%3Dpla-154774696569
Here's a guide on how to do it on a 5. Can't seem to find one for a 6