Katniss will find the majority of villagers willing and eager to trade with her for the meat - the forest is a dark and terrifying place to them, and most of the people with the bravery to venture into it are dead now. So she'll probably find herself being well-stocked when it comes to goods in trade (or currency if she ends up accepting it, because there is currency!), by virtue of there not being a whole lot of other people providing game.

However! She will find that while some few of the hunters family might accept her offerings, there are a few who will refuse, and one in particular will probably start yelling at her about taking advantage of a poor family's destitution and being a thieving, good for nothing charlatan. This one in particular is called Therese Goodman, and she's taken the position that any Hero hunting is taking advantage of the sudden paucity of labour when it comes to hunters. Basically, the Heroes killed her husband and then took his job and are now trying to buy her off and Katniss just got to be the focal point of that.

Way to go, Katniss.