Only a small ding
It is true that closing credit accounts may lower your credit score. When you close a credit account you may shorten your credit history, lower your available limit and raise your utilization. That may hurt your credit.
However, if you keep low balances than your utilization will remain low. Also, if it’s NOT your oldest card then you don’t shorten your credit history by closing it.
Even if it’s your oldest card, as a rule of thumb it’s worth keeping the card only if it’s older by more than 4 years than the other cards.
Unused cards contribute nothing to your credit anyway (what build credit is a stream of timely payments), so you loose nothing by closing it.
Conclusion: If you don’t plane to use the card – let them close it. You may see a few point drop in your score, but after a month or two your score will get back to where it was.
Only thing – make sure you have some kind of written confirmation that the account was closed with $0 balance, and keep it forever (here’s why).
See close-credit-card.html for more information.