To my knowledge, this is the only title of the Virgin or devotion to Our Lady directly related to Islam:
The Blessed Virgin appeared to Saint Peter Nolassco, to his confessor, Raymund of Pennafort, and to the king, and through these three men established a work of the redemption of captives. She desired the establishment of the Mercedarian religious order. (derives from the Spanish word for mercy - merced) Its members would seek to free Christian captives from the Moors and offer themselves, if necessary, as an exchange. The complete name of this order is: Order of the Blessed Virgin Mary for the Ransom of Captives (OdeM).*
The Order was legally constituted at Barcelona by King James of Aragon was established in Spain and later approved by Gregory IX under the name of Our Lady of Mercy. St. Peter was the first superior, with the title of Commander-General; he also filled the office of Ransomer, a title given to the monk sent into the lands subject to the Moors to arrange for the ransom of prisoners.Today, who can we send?
Requests of Our Lady to St. Peter Nolasco - August 1, 1218:.
The Blessed Virgin Mary:
“Find for Me other men like yourself, an army of brave, generous, unselfish men, and send them into the lands where the children of the Faith are suffering.”
St. Peter Nolasco:
"Who am I that God should honor me like this? And who are you, who knows so well, the secrets of my heart?'
The Blessed Virgin Mary:
"I am Mary, the Mother of God. My son, the Redeemer of the world,
who came to give liberty to the captive, has many people bound in captivity, and wishes the order to be established." - Source
There is no one to take the place of prisoners these days. Today there is no bargaining with terrorists. Neither is there any real defense enacted for Christians suffering in Pakistan, Nigeria, Syria, Iran, Iraq and other Muslim countries. In the time of St. Peter Nolasco, ransom would be paid to free those held captive and forced into slavery, and failing that, the Mercedarians offered themselves in exchange for those held captive. St. Raymond Nonnatus, the successor of St. Peter Nolasco, after running out of ransom money, exchanged himself for the freedom of a captive soldier. The Saint was enslaved for a time, and the Saracens pierced his lips with a padlock to prevent him from speaking about the Catholic faith. St. Raymond was later ransomed by his fellow Mercedarians.
Another interesting factoid about devotion to Our Lady of Ransom - or Our Lady of Mercy as she is known since Vatican II: During the English persecutions under the reign of Henry VIII and Elizabeth I, devotion to Our Lady of Ransom enjoyed a greater fervor in the hopes of bringing the Church of England back into "Our Lady's Dowry".
In our day it seems to me it would be good if the devotion was revived and given greater attention, considering the continued threats of terrorism, and above all, the ongoing persecution of Christians in Muslim lands. Our culture is faced with many moral afflictions as well, such as addictions to vice and various obsessive-compulsive disorders. Our Lady of Ransom would seem to be an efficacious title one might use to implore the Blessed Virgin's help to obtain freedom from those sins which most ensnare us.
Prayer to Our Lady of Mercy
Blessed be Thou, O Mary, the honor and the joy of Thy people! On the day of Thy glorious Assumption, Thou didst take possession of Thy queenly dignity for our sake; and the annals of the human race are a record of Thy merciful interventions. The captives whose chains Thou hast broken, and whom Thou hast set free from the degrading yoke of the Saracens, may be reckoned in the millions. We are still rejoicing in the recollection of Thy dear Birthday; and Thy smile is sufficient to dry our tears and chase away the clouds of grief. And yet, what sorrows there are still upon the earth, where Thou Thyself didst drink such long draughts from the cup of suffering! Thou alone, O Mary, canst break the inextricable chains, in which the cunning prince of darkness entangles the dupes he has deceived by the high-sounding names of equality and liberty. Show thyself a Queen, by coming to the rescue. The whole earth, the entire human race, cries out to Thee, in the words of Mordochai: "Speak to the King for us, and deliver us from death!" (Esther 15: 3)
*Similarly, St. Felix of Valois founded the Trinitarians for the Redemption of Captives.