Cloth evaluation aside, a more basic question is how does one know this was “Our Lady of Guadalupe”? The story and the resulting good fruit are very compelling. While, generally speaking, the Church accepts this event as miraculous, and while Pope Benedict XIV pronounced Our Lady of Guadalupe as the patron saint of Mexico, no Catholic is obligated to believe in this miraculous event.
But I do.
From the Story of Our Lady of Guadalupe...
Then he climbed the hill, to see from were he was being called. When he reached the summit, he saw a Lady, who was standing there and told him to come hither. Approaching her presence, he marveled greatly at her superhuman grandeur; her garments were shining like the sun; the cliff where she rested her feet, pierced with glitter, resembling an anklet of precious stones, and the earth sparkled like the rainbow. The mezquites, nopales, and other different weeds, which grow there, appeared like emeralds, their foliage like turquoise, and their branches and thorns glistened like gold. He bowed before her and herd her word, tender and courteous, like someone who charms and steems you highly. She said: “Juanito, the most humble of my sons, where are you going?” He replied: “My Lady and Child, I have to reach your church in Mexico, Tlatilolco, to pursue things divine, taught and given to us by our priests, delegates of Our Lord.” She then spoke to him: “Know and understand well, you the most humble of my son, that I am the ever virgin Holy Mary, Mother of the True God for whom we live, of the Creator of all things, Lord of heaven and the earth. I wish that a temple be erected here quickly, so I may therein exhibit and give all my love, compassion, help, and protection, because I am your merciful mother, to you, and to all the inhabitants on this land and all the rest who love me, invoke and confide in me; listen there to their lamentations, and remedy all their miseries, afflictions and sorrows. And to accomplish what my clemency pretends, go to the palace of the bishop of Mexico, and you will say to him that I manifest my great desire, that here on this plain a temple be built to me; you will accurately relate all you have seen and admired, and what you have heard. Be assured that I will be most grateful and will reward you, because I will make you happy and worthy of recompense for the effort and fatigue in what you will obtain of what I have entrusted. Behold, you have heard my mandate, my humble son; go and put forth all your effort.” At this point he bowed before her and said: “My Lady, I am going to comply with your mandate; now I must part from you, I, your humble servant.” Then he descended to go to comply with the errand, and went by the avenue which runs directly into Mexico City. - First Visit
It's a wonderful story but it does not call attention to God once (as is often the case). This is not in keeping with the scriptures in which all things bring glory to God. But, as you can see from the story, God and our Lord Jesus is rarely mentioned.
One has to wonder why Mary would asks for a temple to be built for her and not to God? No one is under obligation to believe this "miraculous" event occur. But one wonders why someone wouldn't raise questions about people popping in on them asking them to erect temples to them.