I don't find any record that the "Mohammedans" attacked Assisi in 1239, or any time during St. Clare's life. The entry in the Catholic Encyclopedia refers to an attack by the army of Frederick II, Holy Roman Emperor and King of Sicily - a Christian ruler, although often in conflict with the Pope.
The original Breviary says "Saracen."
"Often in conflict"? Boy, that's putting it mildly.
From Wiki, this may shed some light on how the Saracens and Frederick's army were not separate entities:
At his coronation, he showed how unusual he was. He wore a brand-new, red coronation robe with a strange ornamentation at the edge. This was an Arabic inscription indicating that the robe dated from the year 528 in the Muslim calendar; it incorporated the Arab benediction: "May the Emperor be received well, may he enjoy vast prosperity, great generosity and high splendor, fame and magnificent endowments, and the fulfillment of his wishes and hopes. May his days and nights go in pleasure without end or change". This coronation robe can be found today in the Schatzkammer of the Kunsthistorisches Museum in Vienna.
Rather than exterminate the Saracens of Sicily, he allowed them to settle on the mainland and build mosques. Not least, he enlisted them in his - Christian - army and even into his personal bodyguards. As Muslim soldiers, they had the advantage of immunity from papal excommunication. For these reasons, among others, Frederick II is listed as a representative member of the sixth region of Dante's Inferno, The Heretics who are burned in tombs.
If nothing else, at least the possibility of Saracens attacking San Damiano is grounded in the reality of the time.