The T&Cs state that if they receive a PCN "that is capable of being paid" from a public or private enforcement agceny they will pay it and then charge the person hiring the car the fine + their third party admin charge.
Such a term is unlawful because the Consumer Rights Act 2015 prohibits unfair terms, and paragraph 20 of Schedule 2 (https://www.legislation.gov.uk/ukpga/2015/15/schedule/2/paragraph/20) provides this example of a term that a court may deem unfair:
A term which has the object or effect of excluding or hindering the consumer's right to take legal action or exercise any other legal remedy, in particular by—(a) requiring the consumer to take disputes exclusively to arbitration not covered by legal provisions,
(b) unduly restricting the evidence available to the consumer, or
(c) imposing on the consumer a burden of proof which, according to the applicable law, should lie with another party to the contract.
As paying the penalty has the effect of excluding your right to exercise a legal remedy (i.e. appeal to the Traffic Penalty Tribunal), the term is invalid.
However the first thing you want to do is contact whoever provided the car to you, and ask them to contact the hire company and tell them (the hire company) that you what to contest the notice to owner and that you will lose the ability to do so if they pay, and ask them not to pay and instead make representations to the council on the ground that the vehicle was on hire, and asking the council to reissue the notice to owner directly to the hirer.
If you signed the hire agreement with the hire company, you can contact the hire company directly.
Unless and until you can get the hire company to agree to this, really nothing else matters.
Of course if you just want to pay, you can go onto the council website and pay right now and that will be the end of the matter.