The link between Peeta and Katniss and their sponsors is a man named Haymitch. He was a tribute and a champion in the hunger games about 24 years ago. It is his job as a former winning tribute to guide and mentor the current tributes. We see that he is constantly drunk and not always the best mentor to Peeta and Katniss. Of course, we have to admit that mentoring children sent to die every year would certainly take its tole on a person. Haymitch has several strange quirks and is certainly a damaged person after his involvement in the hunger games for so many years. However, as the only living winner from district 12, he is all they have. Haymitch can seem cruel at times but he is actually a very intelligent man. Katniss is able to understand what Haymitch is guiding her to do through the packages he sends to her. For instance, she receives soup for Peeta after she kisses him. One kiss equals one bowl of soup. When Katniss kisses Peeta again and does not receive a package, she knows she must step up the act in order to gain more sponsors.
In the beginning/ middle of the book Katniss states that to get gifts from their sponsors it has to go through their mentor first, which means that it has to go through Haymitch to get through to Katniss and Peeta in places such as the cave.