Pick a set of numbers. Then note the highest and the lowest number in the set. Together, those two numbers represent a range, which includes all the numbers in the set. A range is singular - you have one single range. An example might be the range of 1 to 10, or 1:10, or 1-10.
The same principle works for dates and times. For example, you might have a parcel due to be delivered within the range of 9am and 10am. Or, you could say, between 9am and 10am.
So when your delivery company says that your thing is due to be delivered between (the singular range of) 13:00-14:00, the correct response should be: Between 13:00-14:00 and what other time range? Or did you mean "between 13:00 and 14:00"? Or perhaps "within the range of 13:00-14:00"?
You might consider this pedantic. I do not. It's an indication of the slow decline of the quality of companies, and how much they care about getting things right. Even big companies like DPD get this wrong. And they should know better, because they have the resources to do better, and they're ubiquitous. Ppeople get used to seeing sloppy language like this everywhere, and assume it's correct, and then it drags everyone else's qualities down too.