If the character is TC, they can keep re-targeting it with Woes in each of their upkeeps. Because the character was played before Woes tried to negate it, the CBP doesn't help.
If the Woes target enters battle (TC or not), Woes doesn't prevent it because that counts as replaying the character. It also counts as replaying the character when it returns to territory.
Basically, Jericho stops Woes from preventing any character that needs to enter battle (as long as the opponent meets the condition for Jericho). But TC characters need to enter battle each turn to "regain" the CBP so they work until the opponent's next upkeep.
If you want to know how it impacts a specific character and the above doesn't help, you can PM me if you don't want to ask publicly.