The scene before he tries to kill Palentine. While at this point his insanity is what's guiding him now, he still takes the time to send a letter and money to Iris after talking her into leaving prostitution. (At the time he didn't know Sport convinced her to stay.) The letter itself while barely visible to read borders on Tear Jerker territory:
Travis: Dear Iris, I hope this is enough for your trip. By the time you read this I may already be dead.
Also, a smaller one in the end, where despite getting angry at and spurned by Betsy before, forgives her and gives a free trip (unless that really was all in his head).