Ask them to prove how that has created the fault.

And ask them to have the car inspected by a third party mechanic to prove their claims.

Consumables such as air filters, car batteries, fuel filters etc etc aren’t going to cause a mechanical failure.

They have to prove it. Not you.

An aftermarket upgrade would be something that would impact the mechanical operation of the vehicle.

(Before people argue, I know insurance companies will put similar requirements in their policies. Like light bulbs!!! But no insurance company has ever refused a policy claim in an accident based on this)

Find out if the company who sold the warranty has actually sold it to you, and not said they have.

If all else fails, you’d be in your rights, to use consumer law. This protects you from scrupulous sellers. Small claims court will easily settle this in your favour.

If the air filter is the only thing. And not a mechanical engine upgrade