Hi, that is a decision that only you can make with your vets advice. I had the bands removed from all 3 of my birds, but kept them in a safe place just in case. The breeder has the corresponding paperwork if they have kept it, some don't. There is no law regarding bands, no real database for bands and identifying birds etc.
The reasons I had mine removed, is because I have read way too many horror stories about birds getting the band caught on something while in their cage and by the time they were found, they have chewed their leg off to get unstuck, or the vet has had to remove the foot. My vet has many stories of birds that have come to him with band/ leg accidents and he highly recommended I have him remove them, which I agreed with after all the research I have found. If you do decide to have it removed, make certain to keep it just in case you ever need it. Others here insist they should stay on I case their bird escapes, it is easier to prove it is your bird, but only IF you keep the band info at home in a safe place. But like I said, there is no national registry that keep that info on hand , so it is up to you.
Oh, and my amazon was always playing with her band, I was afraid she would irritate it after time.
Good luck with your decision, and keep us posted.