To first answer your question, one needs to understand what purpose an allusion serves in literature. According to the eNotes site, an allusion is
a reference, usually brief, often casual, occasionally indirect, to a person , event, or condition thought to be familiar (but sometimes actually obscure or unknown) to the reader.
Therefore, sometimes it takes knowledge on a reader's part to recognize an allusion in a text. When one lacks the knowledge to understand the allusion being made, the allusion can be lost to the reader.
In regards to Eliot's "The Waste Land," there are multiple allusions made regarding Madame Sosostris's tarot card reading. Readers need knowledge of tarot cards and their meanings for the allusion to make sense.
1. "The drowned Phoenician Sailor"--This is not a typical card seen in a traditional tarot card deck. The allusion to the drowned sailor references death and foreshadows the Phlebas who drowns later in the poem.
2. "Belladonna, the Lady of the Rocks"-- Again, another card created for the poem. Here, Eliot could have been alluding to Da Vinci's "Our Lady of the Rocks." The significance of the card lies in the fact that it represents rebirth and purification. Eliot knows that for the Waste Land to survive a rebirth and purification is needed.
3. "The Man With Three Staves"-- This card can be associated with the Fisher King (a reference to the fact that no man can change all around him on his own). The allusion can also be made that the card represents a journey. Again, this reference points to the fact that Eliot wishes the Waste Land to be changed and only a journey to find spiritual newness will allow this to happen.
4. "The Wheel"-- This card can be justified in two very different ways. First, the idea that the Waste Lands exist in a constant circle: day and night, season to season. Second, the wheel could represent a time for change. By turning the wheel, one can be making a decision to change in their life.
5. "The One-Eyed Merchant"-- This is another card not found in the traditional tarot deck. The one-eyed merchant card could reference the closing of a single eye because of fear of what one will see. While only one eye remains open, it could be simply to suggest existence.
6. "The Blank Card"--Again, this is an invented card. This card could represent many different things. First, the fact that if nothing changes in the Waste Lands the Waste Lands will fail to exist. They will become blank, non-existent. Another interpretation of the blank card can reflect the imperfections of the reader, Madame Sosostris. The fact that a card with nothing on it could be seen as the fact that she could be wrong about her reading, that she cannot control fate or another's chosen path.
7. "The Hanged Man"-- While typically denoted as negative, this card can actually have a positive understanding. The changing of ones position in life could represent the fact that they are willing to change how they look at life in order to change life itself. The hanging man card can also be used to depict the inability to do anything about the Waste Lands. Given the man is hung, he is unable to move from the position. Instead, he must stay where he is at and watch.