Whether to ask or not to ask?
Ask, if you feel you and your team deserve it then by all means give your manager a nudge. It sounds like you have a manager who isn't very interested in team morale, this needs to change for obvious reasons.
But if you don't ask, you'll get nothing except a bitter taste in your mouth every time others quite rightly and proudly brag about their rewards. At the very least it will start the manager thinking about it. The positives outweigh any possible negatives (I can't actually think of any). You're not asking for anything out of the ordinary, the company already has a reward system in place. You and the team should be benefiting from it.
How to ask? I'd just be straight up about it when I get a chance, ask him/her straight out politely why you and your team never get any rewards like others do. Is it because those rewards don't apply to your team? Is your team underperforming? Stuff like that. Put the onus on the manager politely to explain why. Don't be confrontational, pose the questions as if you're asking for guidance to improve performance.