Do minor improvement actions have any meaning in the family version of Agricola?
The rules are pretty clear, the Minor Improvement cards are not used, so you ignore it.

Agricola as a Family Game (for 1-5 people from 10 years)
In the simplified version of Agricola, the Occupation and Minor Improvement cards are not used - players do not have a hand of cards.
The first game board is turned face down, showing the &quot;Agricola Family Game&quot; side, and in a 3-5 player game only the &quot;Family Game&quot; Action cards are used.
The Major or Minor Improvement action is restricted to Major Improvements.
Otherwise, the rules are the same as for the full game.