Reducing your credit limit does two things. It reduces your overall borrowing ability, and it increases your current debt as a percentage of your total borrowing ability. Both of these can cause your credit score to decrease, although the effect should largely be temporary. Unfortunately, canceling your card in retaliation will further reduce your borrowing ability as well as potentially increase your utilization, and it may also decrease the length of your credit history, especially if this is one of your older accounts.
You may want to use the card occasionally if you still shop at Target, provided you keep your maximum monthly balance to less than 10% of your credit limit, and you pay it in full every month. Otherwise, just leave it in your wallet or desk drawer, until you really need it, and forget about short term fluctuations in your credit score.
