I have worked in offices were they provided rewards for metrics. More notably this is usually done in call centers to keep people motivated in my experience. With that being said, it depends on the reward. If it's, say, a lunch pizza party for your department, I am sure some are asking in hopes you invite them along (usually more aimed at friends who are in other departments than random people you have not met).
Other times it's just people generally curious. I have been on both sides of the court for this one. When I have asked others similar questions, it was because we were in a mutual break location and they happened to be someone who was brought to the attention of the office.
Oh hey! You are the one who won this month's reward! When are you going to do it? (or even ask where if it's a lunch with the boss).
Nothing is really implied by me asking and I am sure others as well. It's mostly a topic to chat about while taking a drink or hitting the vending machine.
Sometimes people are new to the company and they want to find out if these rewards are really worth working towards so they ask about it.
You never really know what the motivation behind the asking is, but most of the time it's just harmless chatter for a quick break. When I have been asked the question, I usually just reply with the truth! If they ask these things the day I was rewarded:
Oh hey! yea that was me! I don't know yet. Since it's something for my dept/team, I want to make sure the others are around too and I haven't had a chance to talk to them yet. Looking forward though to eating some Pizza from Valencia's though! Favorite pizza in the area! Have you won before?
Or if it's more of a 1 on 1 lunch treat
Oh hey! Yea that was me! The boss usually like's to take us to Durant down the street. He usually makes the plans for Fridays but we have yet to talk about it! Have you won before?
It's just simple office chatter. Maybe some of them are jealous of it, but again, you can't really know people's true motives. All you can do is just go with it and chalk it up to office chat. If it's a few days after the reward I would usually reply letting them know the plans. There really is no harm in it.
If it's a group thing and someone tries to sneak in, the person who doesn't belong is usually turned away... but I have also been invited to grab some food from a department party where there were too much food. Either way, that's something out of your control.
So again, I would just go with it, answer like idle office chatter and have some fun. There are a lot of reasons why people ask, and usually, they are not malicious.
Now that I am more aware of the prize due to your edit, it's still likely people are just trying to give you friendly banter. Any time someone wins a giftcard, it's usually a common joke people throw out about "where's the party" implying you will use the gift card to spend on the team. It's more jokes than anything, but I am sure some mean it down inside somewhere. Again, you can only control your response to them and you can't control other's jealousy. Just have fun with it and kindly dismiss yourself.
Party? (jokingly) No way man, that amazon giftcard is going towards me buying a new coffee maker on amazon!
Just have some fun with it.