To the dog owners out there (read description plz)

pic is a wip for Shiia on FA, art is mine character is not

I have a mutt dog, he's poodle,pug, cocker spaniel and something else (i know rite?) He's about 6 months old and like 40-45 pounds. I got him about a month ago from a friend of my mother and the people that had him before us had never walked him on a leash. He's made great improvement in the last month but he still likes to eat stuff off the ground when i walk him which he then vomits up later. I was told by my sister that when he tries to eat something to yank on the leash to pull him away from it. From what i can tell it's not hurting him because he still tries to get at w/e he's trying to eat and he doesn't get aggressive or whine, however there's always at least one person who tells me to stop choking my dog (which i'm not!). I dunno, is it wrong the way that i'm handling the situation and if it is what is the right way to correct this behavior? Thanks in advance.