The central point of this skit is, of course, to illustrate that the Colonels are ill-educated "fools": neither has heard of one of the most famous poets of the 20th century. But any famous poet would do for that: why Eliot?
The biggest reason simply seems to be that Heller, the author of Catch-22, was a fan. Heller taught English at college, and Eliot would have been a common part of the curriculum. Letters sent by Heller quote Eliot as an inspiration, saying that The Waste Land was "always present in my awareness".
Heller also quotes Eliot in interviews:
T.S Eliot said that when one is forced to write within a certain
framework, the imagination is taxed to its utmost and will produce its
riches ideas. Given total freedom, the work is likely to sprawl.
- Conversations with Joseph Heller by Joseph Heller
Critics and biographers have also claimed thst Eliot was often a consideration when Heller was writing:
The notion of playing off an aggressively modern idiom against a
familiar biblical narrative clearly looks forward to God Knows, but
Heller abandoned the idea apparently when he remembered T. S. Eliot
had already done something along these lines in 'The Journey of the
- The Fiction of Joesph Heller by David Seed
It is worth noting that this reference to T. S. Eliot in Catch-22 is not isolated. Over the following two pages, it is repeated eleven times. Heller wants us to remember the name.
Eliot has been both praised and criticised for the obscure, ambiguous nature of his poetry. His contribution to literary criticism reflects this, arguing that any art can only be understood in context of previous art and that while poems may have a stated meaning, non-subjective judgments by readers are equally valid. In the book, the colonels treat the name as though it is some sort of puzzle, which would seem to be a fitting metaphor for the way in which critics (and Eliot himself), treated Eliot's poetry.