As such I will say that the Danish press barely cares. In fact this site was the first place I heard about the incident. I doubt it will do much to the relationship between Denmark and Finland, which mostly is one of friendly indifference.
Friendly indifference?
I would think Danes and and Finns would have a lot in common. For instance, the first thing you think of when you wake up in the morning is, "Thank God I'm not a Swede!"
But that's the problem we don't have much in common beside that, and our relationship to Sweden is quite different, when we hate Swedes we do so as a hobby, while the Finns do it as a national sport.
The only thing we have really in common is our love of alcohol, and while that makes Finns funny to party with, it makes the talks afterward a little embarassing. Swedes and Norwegians are much easier to deal with because they never remember anything the day after.