I have a card that states that leaving group strength increases as bond between carbon and leaving group decreases. I thought it was the other way around.
Your card is correct, I think. As the bonds between a carbon and a leaving group DECREASES, the strength of a leaving group becoming independent increases. In other words, if a bond is DECREASING in strength, it WEAKENS and there's a higher chance it will ACTUALLY break. The semantics of it all may be confusing you.