If you have 80 points in Barter you can convince him to pay a bit more or convince him to just be happy with killing one of the two Gunderson’s (although it’s just as easy to get both of them). With this information, you can go back and talk to Walter. This starts “Beyond the Beef” and it is the best way for you to quietly kill Heck. If you agree to work for him, you can start the quest by going to Heck and learning about son, Ted. If you can pass the Speech check, you’ll be able to convince him that he should really just go home before he crosses the line.
In order to get him to actually abandon it, you either need high perception or 75 points in Speech. You can open this path by talking to Ethel and agreeing to help her convince Walter to abandon his quest for revenge. If you don’t want to kill Heck or Ted Gunderson, you can just use this path to wrap the quest up peacefully. He wants to make him suffer, and we’re in a good position to help. Even if you fail the persuasion test, he’ll tell you that he’s there tracking Heck Gunderson as he negotiates at the Ultra-Luxe. If you talk to Walter, you can ask about him and learn about his reason for coming to New Vegas. You can find Walter Phebus and his wife Ethel walking around the outside of the NCR station and the Ultra-Luxe Casino.