Q: Made or have made 
I don't think they made a reservation
  I don't think they have made a reservation

They 'have made' a reservation sounds good to me. 
What is the difference. Why is using past sentence in this sentence correct?

A: They are both correct, but in British English the present perfect is used more than in American English. The past simple focuses more on the past action and the present perfect focuses on the present result of the past action, which in this case didn't take place.
