A quick google image search led me to believe what's meant by "borsa di ghiaccio" is an "ice bag" or "ice pack", not just some bag filled with ice.
what would be the difference between a bag "made of" ice, or a bag "filled with ice"
I think you could say "una borsa fatta di ghiaccio" or "una borsa riempita di ghiaccio."
It just says, bag OF ice. We assume, of course, that it's a bag filled with ice, because a bag made of ice sounds impractical. But maybe it would be different if you were to mean a bag MADE of ice.
Since the word "borsa" also means "purse", a multiple choice with photos would have been nice!
it would have been better to introduce "borsa di ghiaccio" as a picture/mutlitple choice matching game similar to the very first lessons.