I think we are talking about an open reed call. The "band" is actually a castration band used to hold the reed to the tone board. They can also be made with a cork or rubber wedge, and some use a plastic wedge as well. The thing to keep in mind with the cork or rubber wedges is the difference between how a predator call and a duck call are "played". With an open reed predator call, you are actually putting your lips on the reed. The wedges sometimes do not hold well, and cause the reed to change positions, which of course affects the sound. If you have a gentle style of blowing a call, you can probably get away with the wedge. But if your calling style is more aggressive, you will want something that will hold the reed more firmly to the tone board. There are some other nuances that come into play with how the reed is held in position as well. You do need something to hold the reed tighter than you would normally find on a duck call.
Al @ THO Game Calls