I'm playing through Mafia III (Yes, very slowly), and I really want to get the silenced pistol Alex used in his Quick Look. It's listed with the arms dealer as "Available as a favor from Burke." Everything I'm reading online after the fact says you can unlock this by giving the first racket you take over to Burke, but I can't figure out if this is the ONLY way to unlock that pistol. Any help? Did I bone myself by giving that first racket to someone else?

You can unlock them for free by giving them the racket and then the whole sector. But you can also buy it later. Don't worry. I was also kinda worried because I don't like being locked out of content in a game. But the only difference is if you get it for free or if you have to pay for it. The only things that get locked out are the upgrades for health, ammo and that stuff.