The term Scandinavia includes Denmark, which is not on the peninsula.
The use to include any country other than Denmark, Sweden, and Norway, is something that will tend to really annoy Scandinavians, as we're generally consistent in that use and it's foreigners trying to tell is what names to use for ourselves.
It may be a losing battle, but it's not one we'll give up on.
The term Scandinavia sometimes includes Denmark. Sometimes not, especially if referring to the peninsula.
There's no English language authority dictating what the word "Scandinavia" does/does not mean. The language is its usage.
The first wikipedia paragraph does a good job breaking it down: https://en.wikipedia.org/wiki/Scandinavia