From 1 april 1871 cut squares from not used postal stationery could be used as franking. This was possible until 12 January 1914 for forreign countries and 1 January 1966 inside Denmark.

4 øre cut square as upfranking of 4 øre postal card

3 øre cut square as franking on postcard

Previously it was common to collect the imprinted stamps from postal stationery in the same way like stamps are collected. The imprinted stamps were cut out and put in albums. 

In Denmark there is very few (if any?) collectors of cut squares. Therefore the value of cut-squares is very limited.