This, of course, was an historical 'leftover' from the Congress of Vienna following the downfall of Napoleonic France. The House of Savoy, at that time the Kings of Piedmont-Sardinia, replaced the French as protectors or, in the old feudal language, Overlords of Monaco which, at that time, included considerably more territory than the modern principality we know today. So, the Kings of Piedmont-Sardinia (who after 1861 became the Kings of Italy) were the overlords of Monaco. At least according to them. Actually, by the time the House of Savoy gained the Italian crown the French were back being the protectors of Monaco as well as by that time having gained Savoy, Nice and surrounding areas from Piedmont-Sardinia in exchange for supporting their struggle against Austria. King Vittorio Emanuele I of Piedmont-Sardinia was the first to gain the overlordship of Monaco, which was then passed to his successor King Carlo Felice and then to King Carlo Alberto and finally to King Vittorio Emanuele II who later became the first King of Italy.
King Carlo Alberto had at first hoped to bring Roquebrune and Menton into his own kingdom and sent troops into these towns during the uproar of the reign of HSH Prince Florestan. As we know, Prince Florestan did have a very monarchial temperment but his son, Prince Charles III, came to a new agreement with the French Emperor Napoleon III. After the 1848 Revolutions, Menton and Roquebrune took up the Italian tricolor and were officially placed under the direct protection of the Piedmontese monarch. That is where the fractions come in. However, King Carlo Alberto met with defeat in his fight with the Austrians and it was his son King Vittorio Emanuele II who himself came to an agreement with Napoleon III, giving up Nice and Savoy in exchange for French friendship and these areas have remained a part of France ever since. Grimaldi rule over Menton and Roquebrune was sold to France, which had the area already anyway, and that is when Monaco took on the shape we know it today, reducing the size of the principality considerably.
Control of areas come and go but titles are rarely changed, even if they are only a reminder of historic glories. The Princes of Monaco, likewise, still have many titles left over from their former place in the aristocracy of the Kingdom of France. Anyway, that is the background of why the Kings of Italy were, on paper at least, still titled Overlord of Monaco, Roquebrune and 11/12 of Menton.