Clarification: String spending to offer xp.

Since the actual list says:

You can spend a string on a PC to:
offer them an xp to do what you want.

Does that mean that if you spend the string, make the offer, and the PC refuses, the string is gone?

That is what the phrasing seems to indicate, but I'd like to confirm it.

that's how I play it: players need to make an convincing proposal

Yes. That is correct!

The other player then has a choice: take the bait, or spurn you to no immediate advantage.