So when an opposing character has an Unfettered token on their card but Superwoman does not have the SP showing, does the underlined effect still work?

I would say no. It doesn't say "even if this power is lost"

examples
It doesn't give tokens though.


All the token giving powers I can think of right now are traits. Which is not helpful.

I have to say that yes, even if the power isn't showing, it still happens for this reason: The SP grants the ability to place the token, its not actually causing the effect.

DarthUr, had the same issue, can only of traits, but this popped in my head

CW: Ultron

SUMMON THE DRONES: Give Ultron a free action if she has no action tokens. Put a CW #002 Iron Man Drone or CW #003 Ultron Drone in your starting area on its 30 point line if less than 4 total friendly characters with those names are on the map.

if she loses the power, she can't make more, but losing it doesnt destroy the ones she already made. Thats why I think the tokens stay in effect. They are already actively there, so they'd be independent from the power

That's 1 for each side.

I agree with both. I'm leaning towards DarthUr because the power causes the effect, however usr makes an interesting point.

I think the token would not go away but the effect from the token would go on hiatus until it returns.

Anyone else?

The token would remain but do nothing since there is currently no effect to define what the token does.

Yup, this.

And let's make it 4 to say that when the power isn't showing, the tokens do nothing.

Anything that says to place a token on a figure's card (Punisher, Superwoman, Speed Force figures, etc) will leave that token on the card until/unless the power also says how to remove one or more. If it doesn't say to remove the token, it stays on the whole game.
The power also has to say what the token does... if that power is no longer in effect (Superwoman losing the power via damage or OW, the figure being KO'd etc), the token gives no effect. If there were ever a way to resurrect a figure on your team that gave the token to the opponent, once they came back on the map, the token's effect would return with them.

No, the power enables the placement of tokens. It does not generate the effect. Tokens on the piece generates the effect. Is the token there? If yes, then the effect is in place.

...you should read the power again.
Unless a power says "even if this power is lost," getting rid of the power (either by OWing it, damaging the figure so they lose the power, or KOing the figure) will remove its effect. It works that way when your opponent OW's one of your powers (OW their OW), when a figure puts up Barrier or Smoke Cloud, etc. When a power is no longer active, it's no longer in play.