How to get rid the sticky part on my card?

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My bank mailed me a reward card several months ago. I wasn't really fond of reward cards, point cards, or something of that sort because I believed that it would only make me spend more than necessary just to earn points. However, a relative advised us to use it because it is very easy to earn points with it. To make a long story short, I was convince of its goodness and decided to use it. A sticker was used to attach the card on the paper. After all these months of just leaving it with the sticker, the sticker left a mark on the card. It was very sticky and I tried removing it with oil. I can't put it in my wallet because it would stick. I always have to put it in a small plastic cellophane to prevent it from sticking to my wallet (and other things). Any suggestions on how to remove the sticky part without damaging the card?