The law referred to seems to be Law Nr 130 of 27 May 1908. According to § 11 in that law, the child of an unwed mother could be given the surname of the stepfather upon providing the marriage certificate and other relevant documents (please see http://www.angelfire.com/music/langgaard/lov130.htm
- in Danish). Maren Nielsen Aarestrup would then be the mother, but Valdemar Falck Løndahl doesn't seem to be the father - at the baptism 7 April 1903 the child's surname is Jensen.
One more change to the reading:f. Nielsen Aarestrup, cop. i Odense Vor Frue K. 3/5 07
The marriage 3 May 1907 in Odense is here:
Odense Vor Frue 1892-1918, opslag 173, Nr. 20