Trivia: Tommy Lee Jones' famous line "I don't care" was scripted, but only actually filmed after much debate, as he didn't like the line at all. According to screenwriter Jeb Stuart, he kept trying other lines instead. "After a while I just said, “Why don’t you just try, 'I don’t care?'" And once he did it, Andy Davis said, "That’s it. Wrap."
Trivia: The scene in which Dr Richard Kimble is first questioned by the Chicago PD was completely improvised. Harrison Ford did not know what the questions would be, which he preferred, as that would allow him to create a more genuine and emotional performance.
Answer: It's a cold compress. You squeeze it, and the inner bag breaks mixing chemicals and it gets very cold. It helps to minimize swelling. He gave it to Kimball for all the bruises he had.
Grumpy Scot