The place where Arthur gets TB in Red Dead Redemption 2 is in the mission Money Lending and Other Sins, where you collect a debt from Thomas Downes. The game tries to force you to do the mission, and locks you into the mission without the option to cancel. This is how to get the secret cancel mission option to avoid getting TB.
0:00 Thomas Downes gives Arthur TB
0:39 The game forces you into the mission
2:20 Enabling the ledger
2:39 How to cancel the mission
5:56 Visiting Mary
6:05 The letter is gone
6:14 Jumping the cliff