Restating: erase each pair of duplicate letters.
For simplicity, start at the left. Scan right to find a match.
THE UNITED STATES ONE HUNDRED DOLLAR BILL
_HE UNI_ED STATES ONE HUNDRED DOLLAR BILL
Repeat, starting again at the left.
__E UNI_ED STATES ONE__UNDRED DOLLAR BILL
The underscores are merely placeholders for spacing.
Any letters remaining?
A
OK, now what?
SpyNavy
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)
This is different from the letter-canceling in post 190. PDJT's message there just demonstrates that you can construct a coherent argument about anything that – if the entire text is long enough – will reduce to a single letter by canceling all multiple instances of a letter. In this case, he wrote a message that deliberately only contained one Q, while making sure all other letters appeared at least twice.