When Katniss comes in to see the sponsors, how do the sponsors/Gamemakers treat her?

They treat her like a toy basically since everyone thinks the hunger games is a game. Katniss has to act well behaved though because they are basically a life or death situation

Since she was the last one to perform her "talents", the gamekeepers ignored her because they were already bored. They had to watch the performances of 23 tributes before watching hers. They act as if she did not matter to them, which in fact is true, due to hunger games being a way for the Capitol to control all of the districts.