Both pieces of work are reactions to post-war trauma, but unlike The Wasteland, which aims to put back together the fragments of Western Literature, fractured by The Great War, and sees the grand narrative ultimately as redeemable/salvageable, Catch-22 seems to almost be mocking Eliot by shrouding his name in a cultural amnesia, paralleling themes of disillusionment and rejection of modernism present in postmodernism.
From Chapter 4:
'T. S. Eliot,' ex-P.F.C. Wintergreen said in his mail-sorting cubicle at Twenty-seventh Air Force Headquarters, and slammed down the telephone without identifying himself.
Colonel Cargill, in Rome, was perplexed.
'Who was it?' asked General Peckem.
'I don't know,' Colonel Cargill replied.
'What did he want?'
'I don't know.'
'Well, what did he say?'
'"T. S. Eliot",' Colonel Cargill informed him.
'"T. S. Eliot",' Colonel Cargill repeated.
'Just "T. S. -"'
'Yes, sir. That's all he said. Just "T. S. Eliot."'
'I wonder what it means,' General Peckem reflected. Colonel Cargill wondered, too.
'T. S. Eliot,' General Peckem mused.
'T. S. Eliot,' Colonel Cargill echoed with the same funereal puzzlement.
For further context, this question has answers that seem to fit my question as well:
What's the significance of the T. S. Eliot reference in Catch-22?