@Natalie503 If the price that was listed for the dates the family enquired about is a price that means you will actually be loosing $ after utilities, other amenities, laundry, etc, then you can just message back, explain how sorry you are, but were green and confused about how to set pricing, and ask them if they'd still be interested in booking if you set the price to what you thought you had it at. On an Inquiry, you, in fact, don't need to Pre-Approve or Decine, just messaging back within 24 hours fulfills the response requirement and you can ignore Airbnb messages reminding you to Pre-approve or Decline. (If it's a Booking Request, you do need to Approve or Decline within 24 hours)
If it's just that you'd hoped to make more $, but you'll still be making some, I'd let this one through and take it as a learning curve. You do need some good reviews to get you rolling, so it will probably be worth it, as long as they do leave a good review. And like you say, you'd feel bad to mess up their holiday. But for all you know, they may have sent out Inquiries to 5 different places, so just because you approve at the price they saw, doesn't necessarily mean they'll follow through with the booking. Inquiries can be like that- you reply nicely, even without a pricing issue, and you never hear back from them.
So if they don't want the booking at the price listed, and let the Inquiry expire, message again asking if they are serious about booking, because you're about to change the prices. Give them awhile to respond, if they don't, then get in there and change the prices or turn off smart pricing.