Turns out the culprit is
https://commons.wikimedia.org/wiki/File:Map_of_Copenhagen_with_surroundings.png
which was used on 45 Wikidata items, as per this query:

#defaultView:ImageGrid
SELECT ?item ?image {
  #image for Skovshoved (item Q12335825)
  wd:Q12335825 wdt:P18 ?image . 
  #Find other items using the same image
  ?item wdt:P18 ?image .
  }

I already fixed this for Rødovre and will do some more of the others as time permits.

I sent out a tweet to ask for help: https://twitter.com/EvoMRI/status/1117104148862898176 .

I looked at https://www.wikidata.org/wiki/Q12317586 (Hvissinge).

A Google image search brings up a few openly licensed images:
https://www.google.com/search?q=hvissinge&tbm=isch&source=lnt&tbs=sur:fmc .
Two of these seem to be in Hvissinge, but I have no good way to verify.
There is also https://da.wikipedia.org/wiki/Hvissingestenen , which is about 1km away and does have its own item.

I set up a Wikidata list to monitor progress: https://www.wikidata.org/wiki/Wikidata:WikiProject_Data_Quality/Wikidata_lists/Items_using_Map_of_Copenhagen_with_surroundings.png