Learn Spanish (Latin America): Tienen que pagar por la demora.

This sentence uses a noun, la demora (the delay), instead of a verb. You use por + noun to say "because of [noun]" or "for [noun]". If you wanted to practice the lesson's grammar and use an infinitive, you could change the sentence to Tienen que pagar por demorar (They have to pay for delaying).

Why do we use por and not para in this sentence?

Por is used for the reason or cause of an action, as well as for exchanges (like paying money for something). The delay is the reason they are being charged. You would use para for a purpose, goal, or destination, like Tienen que pagar para entrar (They have to pay in order to enter).

I usually use tarde for being late. How is demora different?

Tarde means "late" and is used to describe when something happens, while demora is a noun meaning "a delay." If you wanted to express being late, you could use the por + infinitive structure from this lesson: Tienen que pagar por llegar tarde (They have to pay for arriving late).

Is que absolutely necessary after tienen?