New Computer question about drive letter

My old computer was drive C: that I backed up with Comodo. My new computer now uses drive E: for the same folders. My question is I want to keep backing up my folders doing an incremental backup without backing up twice what I had. My question is does it matter if my old folders were C: program files… and now they are E: program files… on the new computer. What I mean is I had a folder on the C: drive that I backed up and restored to my new computer on the E: drive. When I go to back up this folder again will it still recognize the same files since they are on a different drive letter.