How do you, if you do, let players spend advantages/triumphs on a skill check where they just need to succeed? Example as Hunter's Quarry or Bad Motivator.

Do you disregard the result since they just needed to be succesful, or do you treat it as per the book with spending advantages in combat?

Could be spending on the usual chart, or some other kind of bonus. Maybe on Bad Motivator, the issue doesn't come up until the key moment rather than immediately, or the bad guys don't notice the issue.

Any way they can think of which relates to the check! Read: As Normal

I think to disregard Advantages and Triumphs would be a disservice to the players. Likewise, ignoring Threats or Despairs would be a disservice to me.

Generally, I treat it as a little more "encounter capital" that the players have to spend.