Visiting (or calling) cards were sent unsealed, often at the end of the year, in accordance with the prevailing social norms. And in Luxembourg up until 1991, three different postal rates applied to these cards, depending on the whether (or how much) handwriting was included with the card.
When this visiting card was posted from Petange to Septfontanes [Simmern] on December 7, 1961, the rates were:
30c - no handwritten message
1.00 F - handwritten message of not more than 5 words
2.50 F - handwritten message of more than 5 words
It appears that the sender paid only the 30c rate for a business card without a handwritten message, using the 30c+10c 1961 Caritas semi-postal as the sole franking. The 4.50 F postage due charged the next day at Septfontaines suggests that the card contained a handwritten message exceeding five words. Based on this assumption, the penalty would have been double the 2.20 F deficiency or 4.40 F (which amount was apparently rounded up to 4.50 F).
Let's be glad postal clerks are no longer inspecting visiting cards to count any handwritten words that the sender may have added to the printed card!