Perhaps the original item was broken and this is it’s replacement.
Walter Del Pellegrino, author of several books on Italian pottery and expert at http://italianpotterymarks.freeforums.org/ where you posted has taken time and trouble to answer your question very politely and very thoroughly.
I had already told you it is not Deruta, giving an example of their mark, yet you persist in this in your posting there.
I agree with Walter’s anaysis which is as follows.
“Are you certain that this was given to your family in 1935?
The mark is that of the Egisto Fantechi pottery in Florence. The company was in existence from 1895 to 1961. Below you will find a link to an article I have written concerning this very important company. The primary design of this piece is called “Cartocchio”. It is Gothic Floral design that was popular around 1450. It consists of scrolled leafs and flower petals surrounded by fine vines and scrollwork.
I am sorry to disagree with your family’s story but this item was not made in the 1930’s but rather much later and in my opinion it is a fairly recent recent piece perhaps dating to the 1970’s or later. The glazes are too vibrant for early 20th century glaze and the overall design is far too loose and too relaxed for the period suggested. I suspect that this an Asian fake. Another clue is the appearance of the numerals on the base. They are not written in a manner that would have been consistent with the manner in which Italians of the period would have written them. I imagine that the pitcher is relatively light (another sign of Asian fakes) rather than the ten or twelve pounds it would weigh if made with native Italian clay. The mark of Egisto Fantechi is a popular logo that has been faked for decades.
Walter Del Pellegrino”